Well, there are different kinds of bands, so that's what's causing the confusion here, I think.
There is a type of over-the-door band set that you can use INSTEAD of a pull-up/chin-up bar. I think you can get a good workout with these, but I have heard from several people that they felt they were missing out on something. You can buy this kind of band on the beachbody site (or elsewhere, but you probably want to start there so you can see what they're recommending).
OR, you can get a doorway pull-up bar (also called a "chin-up bar") for about $30 from any sporting good store. I have one of these and the installation was simple. The bar itself is very sturdy because it's screwed into the doorjamb - that's what makes it stable. It isn't as intrusive as it sounds, though; I think it has all of 10 little screw holes which can be easily spackled when it comes down.
Then, there are ALSO bands (the Iron Woodys pull-up assist set) that you can use WITH the pull-up bar for an assisted pull-up. Some people seem to really like these, but IMO they're kind of pricey (about $60 or so). It may be a good idea for you to get the bar installed first and try your pull-ups with a chair to see how that feels for you. If that assist feels too awkward, then you'd get the assist set.
Hope that helps. P90X is an awesome set and I am really enjoying the rotation. Like you, though, I spent a lot of time being confused about the equipment prior to purchase. It's spelled out for you really carefully in the set documentation, though.
Good luck!!
Marie