This is a good essay I've seen assigned in classes that use his book

Either analysis is possible-- you could say that it's possible to modify a noun with a noun (and add the appropriate PSRs), or you could say that in those instances the N becomes an A and use the normal AP rule.
The distinction, which you can work out yourself if you'd like, depends on distributional criteria.
Consider, for example:
*The very water fountain.
The very large fountain.
*The linguistics student is better than the physics one.
The nice student is better than the mean one.