Kind of yes and kind of no.
When the initial Yellow Ribbon came out only a few schools dived straight in. The others were more tepid and kind of looked around at the landscape to see who was doing what. After all, there was little incentive for HBS to get in if the highest ranked school that was participating was Haas (a very good program, but one that a lot of guys would pass on for HBS with the expectation that HBS will yield dividends that will offset this initial loss).
The guy giving the briefing also indicated that if you're Yellow Ribbon you stand a lesser chance of getting other financial aid from the school. Consider the following two scenarios (let's just assume YR is $18K per year):
We'll say a year of B-School at Stanford GSB costs $50K.
Scenario 1 (GI Bill + YR + School): GI Bill gets you 18K. Now 32K remains to be split among the school and the YR program. They split down the middle and so the school forks over 16K.
Scenario 2 (GI bill + Financial Aid + YR + School): GI Bill gets you 18K. School offers 10K in Financial Aid. 22K remains to be split among the school and the YR program. They split down the middle so the school provides another 11K. 10K + 11K = 21K.
For school, Scenario 1 better than Scenario 2. After all, why not tap theVA for every dollar you can get if you're the school? The school can then take the money that they would have given you in Scenario 2 and offer that to someone else that doesn't have VA support, leave it in their financial aid pot for next year, etc.
Though not related to business school, I learned that some colleges actually raised tuition in states with a lot of military people because they realized they were leaving money on the table. If your tuition didn't tap the full amount that the GI Bill was willing to cover then, as a school, you were not getting all the money you could get. This seemed like a stretch to me because there are a wide variety of factors that go into tuition hikes since they affect all students at an institution and you might conceivably deter some students from coming. Alternatively, if your school only really costs $15K and you raise tuition to $18K for everyone then even if there are fewer students than can afford it outright, you now have an extra $3K from those that are paying that can be allocated to help those students that might not be able to afford it...or so the theory went.
It was kind of hard to get anywhere in the briefing because all the JAGs, being lawyers, were constantly peppering the guy with questions.