Tax Question - Grad Assitant

Quick tax question, I hope.
Long story short, wife is a GA (school pays tuition & cash each month) and I did not look at her check stubs throughout the year.

University is paying her a monthly check and in this check they are also including other gross taxable income. This other amount looks to be equivalent to the cost of her tuition & etc. Needless to say the other amount is about the same as her net pay. So her gross income at EOY was double than I was anticipating....

Questions:
1. Is the accurate reporting on the university side?
2. Anyway the tuition portion can be tax exempt?

Looks like I will be changing her W-4 to cut her net pay in half to be sure the taxes are covered.