Age is irrelevant, and the student can get Direct Loans at 17. School is wrong on that one.
There should also be no loan application for a Direct Loan (if there is a school form to complete, that is different - I use one for my students, since they don’t have an option to accept online - in that case, the student can tell the school he made a mistake on the DL). The student may have been completing the Master Promissory Note & put it there … he can just do a new MPN with the correct info.
I am a little concerned that the student may have completed an online Parent PLUS loan application … you might want to see what he filled out.