Not a US citizen, but AFAIK, a course includes lectures, office hours, assignments etc. How did he manage to fully understand the materials without all the resources that are provided only for registered students?
Also not a US citizen and I don't know how it works at Princeton, but in my experience, getting actionable feedback on assignments is rare. You may get told where your mistakes are, but not how you should have done it instead. Most of the value of assignments is in simply doing them; that forces you to review the necessary material.
As for office hours, I never went to any, but I assume that they're not going to check your student ID, just as they don't check before lectures.
At my UK uni (some time back) we had tutorials and "office hours". Tutorials would recap lecture material and have question/answer sessions, and set "homework" questions; and be optional. Office hours would give chance to talk with the professor, you just queued outside, or signed up for a time slot.
Tutorials were run by TAs recruited from the body of PhD students and so could be of mixed quality (my metaphysics tutor was better than the lecturer), but would at least have value in repitition.
Libraries were vital to me. As at the time were computer facilities (MathCAD, Maple, Excel, Fortran, etc.). For some of my courses there were laboratories (material science), and for Art History there were trips and a special picture library.
You could sit in the back of lectures back then, but I think they check your ID nowadays.
> Most of the value of assignments is in simply doing them; that forces you to review the necessary material.
Preach it. The same is true of past or specimen exam papers or textbook questions. Writing, like debating, exposes your own ignorance to you and allows you to remedy it.
As for office hours, I never went to any, but I assume that they're not going to check your student ID, just as they don't check before lectures.