You are correct. It isn't just professor salaries. It's not even the bulk of it. It's facilities, programs, and administrators, etc., and like I mentioned earlier, TAs and adjuncts get paid very little even with sky-high tuition.
There have been some studies related to the impact of student loans and available credit on tuition. Here's an article discussing some of it.
Link. Frankly, the availability of huge amounts of credit at below market interest rates is only part of the problem, because it's what enables the problem. The demand is also an issue. I'm a big believer in prioritizing trade programs in high schools. Students shouldn't have to choose between college and aspiring to be the night manager at a Wendy's.
It's the classic third-party payer with unlimited resources problem - same thing that happens with health insurance and pretty much all insurance. The body shop that charges you $400 in cash to fix your fender will charge your auto insurer $1,000 for the same work.