That is true at the graduate level. If you pursue a PhD in life science, physical science or computer science your tuition is waived and you (usually) get a stipend. If you want a PhD in liberal arts you have to pay tuition.
Let me stress that since Rariel brings it up below: nobody pays tuition (again, except non-US citizens).
People take out loans for extra money (the grants and TA stipends ranged in the 9,000-12,000 dollar range per year in my time, 1992-1997), but nobody pays their tuition. One standard joke was that we were so much better off than the professional students (Business, Med School, Law School) because they did pay tution. I never paid a dime in tuition and finished graduate school with nothing more than mild (< $3,000) credit card debt.
I have no reason to believe that this system has changed. Do you have any sources for your claim?