Your first guess is right. If you get free tuition for any reason (including tuition waivers for veteran service), then you either not benefit, or much less benefit from the new Post 9/11 GI Bill.
The new GI Bill pays for the actual cost of your tuition, up to a maximum, and sends the money directly to your school, as you mentioned. So, if the tuition is zero, the money from the GI Bill is zero. However, if you do use the GI Bill, while you won’t get the tuition money, you may still be able to get the book stipend, which is up to $1,000 per year, and the housing stipend, if you are taking classroom courses as opposed to online courses.
Note that this is only an issue if you are in a program that eliminates tuition; if you are using a scholarship that pays to you, then you can use that on top of the new GI Bill.
This is one example of a situation in which the Montgomery GI Bill may be a better choice than the new GI Bill. Of course, one possibility is to use the GI Bill first, and then apply for the tuition waiver for courses after you use the GI Bill up.