You’re half right.
I do concede that the tuition waiver has value. Furthermore, i concede that getting the tuition waiver does, indeed, mean that i’m getting a benefit that makes it worthwhile to do the degree.
But the fact that the university lists the tuition at $30,000 a year ($100K+ total) does not mean that the tuition is worth $30,000 a year ($100K+ total) to me. If it were worth that much to me, i’d be willing to pay it. The fact that i (and every single humanities grad student i know) would not have done the degree without the waiver suggests that, whatever nominal value the university places on tuition, it is actually worth less than that to me (and to everyone else i know).
I agree that is is wrong to simply say (using your numbers) “We get $15,000 a year” and imply that this is the only benefit that grad students receive. As Carmady suggests, arguing that “We get $15K a year to live on” would be more accurate. But i don’t think your formulation, which would require the students to say, “We make $45K a year,” as if the $30,000 waiver were somehow instantly convertible into whatever type of income you desired, represents the situation accurately, either.
The thing is, in economic terms, something is only worth what someone is willing to pay for it. At my university, every single PhD student (in the humanities, at least) gets a tuition waiver, because the university knows that people will not pay $30,000 a year for a humanities PhD. The university can put on its paperwork (and indeed they do) that the waiver is worth $30,000 (actually, it’s now about $38,000, having increased considerably faster than inflation), but that doesn’t mean that’s what it’s actually worth to the people who get it.
If i give you something, and tell you that i have valued the object at $30,000, is my valuation objectively true, even if you would not pay 30 grand for it?