They Do, their channel (in the USA) is a partnership with Discovery Networks, one of the largest, cable media networks , hence the Name, "Discovery Family". They also manufacture toys under license for both Viacom, who owns nickelodeon, and Disney.
Internationally, Network Distribution of Hasbro's Shows is handled through Turner Brodcasting, Time-Warner's Network Brodcasting Division.
So, yeah, they have agreements and partnerships with pretty much all the major players.
People seem to underestimate how large a company Hasbro truely is. They have a monopoly on board games (no pun intended), and they are currently the largest Toy Manufacturer in the world. Along with pretty much nearly every board game brand under their belt, (like Parker Brothers, Milton Bradley, Selchow & Righter, and others), and popular toy lines like NERF, Super Soaker, Play-Doh, as well as their action figure/doll lines based on Both their properties and others, like Disney (including Marvel Comics and Star Wars) and Nickelodeon They also own American Greetings, the Second largest Greeting Card maker under Hallmark. Sure, their In-House Animation Studio is relatively new, and they are relatively small on this front, but they are still a HUGE company.
Its a possibility, considering the slump that Mattel is experiencing, if things continue like that for Mattel, Hasbro may be able to just outright buy them, either way, Hasbro will be the Controlling force regardless.