If you haven't heard of this yet, read on. Taken from this website for your convenience. Thoughts at the end.

14th-15th Century, Brave

It all starts with Merida discovering "the-will-of-the-wisps" (magic). The Magic turns her mother into a bear. This magic is why animals and inanimate objects (brooms & tools) behave like humans. Magic was utilized by a witch, who mysteriously vanishes through wooden doors.

Eventually the Magic from the will of the wisps would lead to the birth of super heroes

1950s-1960s, The Incredibles

Superheroes maintained order in the world. But Buddy, a wannabe superhero, created two things for the demise of superpowered humans: self serving A.I. bots like the "Omnidroid," and the high tech Zero Point Energy (electromagnetic energy that exists in a vacuum). This is the pivotal moment where we see machines eradicating their only threat−supers.

Eventually, toys start to absorb and draw their powers from Zero Point Energy, unseen energy that travels in wavelengths.

1997-1998, Toy Story

The first signs of life from toys are now present due to Syndrome's technological prowess. Toys (sentient objects) come up with a code of rules and learn that human love is another energy source, upon which they thrive.

These toys discover what happens to toys that are isolated from humans.

1999, Toy Story 2

The toys discover that it is dangerous for them to be isolated from humans. We start to see inanimate objects question their purpose in life. For example, Jesse resents her owner, Emily, for abandoning her.

Resentment towards humans was not only carried by inanimate objects but by animals as well.

2003, Finding Nemo

In the ocean we find that fish are incredibly advanced (they have schools, a network and freeway system). We discover that humans are polluting the earth and experimenting on them. Dory was one of the animals that was experimented on, which is why she is forgetful. There are signs of resentment growing towards humans for polluting the environment, stealing fish and caging them.

Animals begin to be more curious and carry more humanistic characteristics.

2007, Ratatouille

In Ratatouille, Remy discovers his love for cooking and displays human characteristics. Some of them are: walking on his hind paws, cleaning his hands, reading, and cooking. This is the first time we see personal interaction between human and animal, but it is for the purpose of controlling humans. Remy controls Linguini because Linguini does not know how to do anything. We see that Remy's rat clan does not approve of the humans and feels both fear and hate towards them.

2010, Toy Story 3

Three years later, toys have gone through a lot with humans. If you've seen the movie you can tell why most of the toys have had it. Being abused physically and emotionally by humans.

Lotso the Huggin' Bear straight up hates humans because they use and discard toy objects like they are nothing. He starts trying to take care of his own kind. This provides yet another reason why machines and objects alike are ready to take over.

Carl and Ellie write to Andy telling him to get rid of his toys because they know the animosity between toys and humans coming ahead, and that's why they are planning on living in solitude.

2011-2016, Up

Carl is forced to give up his house to a corporation/BnL because they are expanding the city. This is foreshadowing−this corporation is the cause for polluting the earth and wiping out life in the distant future, as a result of technology overreach. Carl discovers that animals can communicate with humans, and sees the bitterness that they have. Charles Muntz effectively trains an army of dogs. This is the start of the tipping point between animals and humans.

Years later, the uprising between animals and humans begins. Who do you think won that war?

2100-2200, Cars

When animals rose up against the humans to stop the pollution, the machines saved the humans and they won the war. However since machines helped humans win, it tipped the balance on Earth. Machines/BnL had to send the remaining humans off into space on a ship called Axiom. All of the other machines were left behind to populate the world and run things.

But how do we know cars took over earth and not another planet?

2100-2200, Cars 2

In Cars 2, cars go to Europe and Japan which shows that its the same planet as all the other Pixar movies. It also shows that there are no humans throughout the world. The world at this time ends up with an energy crisis as oil is the only energy used for cars.

Allinol corporation was using green energy as a catalyst for a fuel war in order to turn cars away from alternative energy sources. That clean fuel could have been used to swiftly wipe out (decommission) many of the cars. Allinol was run by BnL which eventually polluted the whole earth due to its use of oil. The whole world becomes unfit to sustain life.

2800-2900, Wall-E

Earth has become uninhabitable for hundreds of years due to BnL. The corporation took over the world/governments starting in the 1950's. Wall-E is the only machine left on Earth after it ran out of resources. He survived because he is fascinated with human culture and also his friendship with a cockroach, which helped maintain his personality and fulfillment. Robots/machines on Axiom (having left earth centuries earlier) show that machines develop a sense of purpose out of the humans' dependence on them. Wall-E is a robot Jesus, and He and his love, the appropriately named Eve, save the human race and start a new beginning on Earth again.

During the credits of Wall-E we see the shoe that contains the last of plant life. It grows into a mighty tree.

2898-3000, A Bug's Life

That same plant we see in Wall-E grew to be the tree in "A Bug's Life". Insects have a longer lifespan in "A Bug's Life". Prior to Wall-E, an ant can last just 3 months. However, in a bugs life, these ants all survive an entire summer and allude to being around for quite some time. One ant states that he "feels 90 again." This indicates that ants are sturdier as a result of evolution and mutated genes. Another ant tells Flik not to leave the island because there are "snakes, birds, and bigger bugs out there." They do not mention humans, because there are very few humans to make it dangerous enough for insects to worry about. However, one kid did allegedly pick the wings off of the homeless bug. Later in the distant future animals start evolving into the dominant species.

4500-5000, Monsters University

Hundreds of years after Wall-E, animals started changing due to radiation caused by BnL. These animals evolved into monsters and accidentally wipe humans off the face of the planet. Monsters University was founded in 1313; this is dated using the monsters' calendar, not the human calendar, and shows that it took place almost 1400 years after "A Bug's Life". At Monsters University, they falsely taught the monsters that humans were toxic and from another dimension. This was because monsters were worried about being erased from existence and altering history.

4500-5000, Monsters, Inc.

Monsters and machines didn't realize their mistake of getting rid of humans until it was too late. They eventually realized that humans were their source of energy, and needed to sustain life. Machines helps solve that by letting monsters use doors to time travel to the human generations.

This leads us to Boo.

∞, Boo

Sweet little Boo never got over Sulley and became obsessed with finding out what happened to him. She remembered that doors are the key to finding Sulley. Later on in life she figured out how to time travel (using wooden doors) and goes back to the source of all magic, "the-will-of-the-wisps" and creates magic to find Sulley by using wood. Boo leaves evidence behind in Brave: two carvings whittled out of wood. They were Sulley and a pizza truck, the two things she loves most in life. Although she knows how to travel through time, she does not know how to determine what time period she will go to. Therefore, speculation has it that Boo is the one planting the easter eggs throughout all the Pixar movies because she has been accidentally going through different time periods.

It's quite a read, but I hope you've taken the time to at least skim through it. In my opinion, as cute a theory as this is, the whole thing started because Pixar likes to put eastereggs in their movies. Not a crazy same-universe concoction, but little things like references to other movies and BnL.

At the end of the day, I'm fine with believing in it because heck why not? Not going to hurt anything. Anyways, just thought I'd post this in case you haven't heard of it. Quite interesting, no?