Star Wars Episode VII Producer JJ Abrams appeared on the The Tavis Smiley Show recently and he discussed one of the concerns many fans have had about Episode VII (and Star Wars in general) being produced by Disney - fearing they will Disney-ify Star Wars. Abrams addressed this by saying,
"The beauty there is Disney doesn't want that. They are well aware of this and they are very careful to make sure that...they are sensitive to that. They don't want that at all, that's the last thing they want. But that company, which is Marvel, they have...it's incredible the scale of that company. They are as aware of that as anyone."
So there you have it. It seems Disney recognizes they have this reputation and is actively trying to disprove it, by trusting and allowing filmmakers on projects such as Star Wars and the Marvel films, do their own thing without be hampered by what the studio wants.
You can watch the entire interview with JJ below, where he addresses much more including his various TV series, as well as his work on the last two Star Trek movies.