Nobody knows for sure outside of the informed circles, but there definitely are restrictions in the contracts. It's not uncommon when doing these kind of international deals for the smaller company to use smarter, more expensive lawyers in order to keep as much control as possible back from the new parent company.
In Henson's case, and this is taking a guess, it seems that while EMTV can make them actually produce new shows, movies, merchandise and advertising - the Henson Company seem to have control of what the actual characters do and how they are presented. Also while EMTV have control of how the Henson programme library is sold and distributed internationally, they seem to have less control over what happens in the USA. Add to that, when these parent companies usually take over they usually replace the more senior members on the board of directors with stooges from their own company, with JHC/EMTV this didn't really happen, they still used people from within Henson. So all in all, even though they own the company, EMTV are still to a degree, on the outside, and apparently (informed rumor time) they are quite unhappy and frustrated about that.
Brian and Lisa are the only ones corporately involved, but i think, as we can take from Muppetfest, it's still very much a family thing and people are still around.