Disney isn't directly making the film, but they can still get their fingers into it through the horrible Hollywood practice called "notes".
Because Disney, or any studio, is the one fronting the cash and is responsible to get the movie into theaters, and people into the theaters to see the thing - they get to review what's going on. The filmmakers will submit scripts, pre-production plans, "dailies" (the raw footage as its being shot every day) and the rough and final edits of the film.
The studio then reserves the right to offer opinions on the work and make suggestions on changes they would like to be made. Because of the internal politics of Hollywood, no one wants to be seen as requiring changes for the most part, so these go by the euphemism of "notes". Who gets to make "notes", and whether someone has to take them seriously or not, is a prime area of power politics all over town. Generally speaking, it comes down to a battle of wills between the filmmakers and the suits trying to get a commercial product.
Filmmakers with a proven record and/or clot can usually talk themselves out of notes; filmmakers just starting out or working under the shadow a previous bomb have ask for a studio note to decide if they will have latte or cappuccino in the morning. On the studio side a suit with confidence in the filmmaker's ability won't issue a lot of notes, but a suit with a lot of confidence in his ability as a filmmaker will issue more notes than an orchestra.
Eisner has a reputation for being erratic in movies just likes he's erratic in the theme parks. Certain projects will simply catch his fancy and he'll delve deeply into the detail of the film. Everyone's heard stories about him going through scripts and re-writing jokes, or passing judgement on costume design or lighting. Other projects, even big budget projects, he doesn't know nor care they exist. It's been said he was all over Treasure Planet and the upcoming Home on the Range - but knew almost nothing of Lilo and Stich until just before its release.
As for Hitchhiker's, I really hope he finds a hobby and stays away.
Hopefully, Disney and Spyglass will hold true to the books (as much as possible) and make a worthwhile movie. There are legions of people out there who know where their towels are and they aren't going to want to see Douglas' work presented poorly. Still crossing my fingers... 
