I believe you have misunderstood. It says:
Generally, qualified education expenses are amounts paid in
2013 for tuition and fees required for the student's enrollment or
attendance at an eligible educational institution.
It then says (emphasis added):
For each student, reduce the qualified education expenses paid
in 2013 by or on behalf of that student under the following rules.
The result is the amount of adjusted qualified education
expenses for each student.
In other words, the "adjusted" qualified expenses may be less than your qualified expenses, but not more. Nothing can be counted in Adjusted Qualified Expenses if it's not counted in Qualified Expenses. Room and board are not qualified expenses in the first place, so you cannot use them to claim these credits. (The part about room and board under adjusted qualifying expenses is saying that, if you can use it for room and board, it is not tax free and thus will not "adjust" your qualified expenses. Basically it is designed so that you either pay tax on it as income, or you can write it off as a tuition expense, but not both, just as in the answer to your previous question.)
The text is also clear here (emphasis added):
However, fees for personal expenses (described
below) are never qualified education expenses.
And then it lists room and board as examples of personal expenses.
Just a general tip based on this and your previous question: I would advise you to give up trying to find ways to garner a tax benefit for your grad student salary (RAship, TAship, stipend, etc.). I'm a grad student also and looked into this in my early years. I know it seems like a tantalizing option, but the credits are not for this situation, so you should lower you expectations about their benefit to you. You're already getting a massive tax benefit by receiving a tax-free gift in the form of a tuition waiver. These tax credits are there to help people who pay for tuition out of their own pocket. If you're not paying tuition out of your own pocket, the credit isn't for you.
(In theory, you could still deduct the price of "books and equipment", but it's unlikely that the amount you spent on these warrants the hassle of maintaining the documentation you'd need. Also, you would have to reduce these expenses by the amount of your tax-free assistance, which is likely to be far larger, leaving you with no adjusted qualified expenses left.)