Probably not out of undergrad. Their financial aid package basically does grants in lieu of loans. They determine your estimated family contribution and then give grants from there.
That's not to say kids don't take out loans. If they estimate that your family can pay $15K per year and in reality it's more like half that, then the student still has the option of taking out loans. But it wouldn't be anything near $150K out of undergrad. Now grad school is different, since the same financial programs are not in place for graduate school and some probably do rack up a lot of debt, but there probably aren't many flunkies getting into med school or business school there and those degrees probably pay off over the long run.
A large portion of their student body probably doesn't get a lot of financial aid anyway since many come from wealthy backgrounds. And with an endowment of around $4 billion (that's
billion, with a b) which works out to over $300K in endowment value per student, they can afford to do what they do. Their financial info is at the bottom of the page on the link below.
ReVU: Quick Facts about Vanderbilt | Vanderbilt University | Nashville, Tennessee
Interestingly enough, one of the kids who did take out student loans was none other than....Dansby Swanson. There's an article today about him in the Tennessean and it talks about him taking a risk going to Vandy when it would've been cheaper to go to other schools.
Dansby Swanson: Vanderbilt's big-league character
I guess that kind of dispels the idea that they're just handing out 30 full rides in Nashville.
But apparently he wasn't as highly recruited out of high school as some others. I'd say he's probably on full scholarship this year...even if not, it probably won't matter since he'll be a millionaire soon.