I came on preparing to join the wrath of those saying of course you can't interfere with your son's university education but after actually reading your OP I don't think YABU. If you wanted uni to meet/discuss your son directly with you you would be, I would 100% agree that your son is an adult, has to be responsible for himself, data protection rules apply, etc.
However your son is paying (whether the actual money is his, yours, or student loan - although tbf if you have paid the full fees upfront I think you have been a bit silly, unless you are absolutely rolling in it it makes much more sense to take out the loan) for a service which includes pastoral support - I can't see why he can't bring along whoever he wants to support him in a meeting as long as he's happy to have you there.
There are loads of equivalent examples where it would be fully acceptable (in fact, encouraged, including many posts I've seen on MN) to bring someone you trust and/or someone who has more experience in a particular arena than you - doctor's appointments, mortgage and financial advice sessions, benefit applications, etc.
Whether these supporters are a partner, parent, trade union rep or friend doesn't really matter - if the individual wants them there and feels it is appropriate then they can be.
Other people upthread have been scornful at the idea of bringing your parent to a job hearing - but at almost every misconduct hearing I've been involved in (part of my job - I'm not just a terrible employee!) the employee has brought someone with them for support, including in some cases a parent.
If you are a student in your late teens it is very likely that your main source of advice and support, whether practically, emotionally or financially will be parents, because most people of that age won't be in a long term serious relationship, or have a social network that may include friends/acquaintances with relevant experience. That comes later as you grow older and develop your knowledge/support network.