A) Education level is not just degree, but also the institution where you got that degree, and B) Stafford loans are not that big actually. For undergrad they are anywhere from 3500 to 5500 per year and cap out at 23,000 total. That is nowhere near enough to cover the cost of education even at inexpensive state school. For curiosity sake I looked up the rates for University of Illinois, the base rate for residents is $12,036 per year. The Stafford loans for the freshman year only cover about 1/4th of that, and that's before all the fees, books, transportation and living expenses. Anything more and the student either needs significant savings of his own, or he needs to work full time while going to college, which frankly is essentially impossible due to time and logistics constraints, or he needs his parents to co-sign private loans. The situation is even worse with private/ivy league colleges where you need to either be in the top 0.001% to get a full rider or you can't attend since no one will give you loan that high.
So no, the "relatively affordable public colleges" and "student loans" is an incredibly dishonest argument designed to underestimate the severity of the problem. The amount of money your family has absolutely does determine the quality of education that you can get in this country. That is not the way it should be. The school admissions should be based on how smart the student is, not on how much money he can pay into the system.