I think there are a lot of privacy laws protecting people from having their records opened (like HIPPA). I think you are not required to disclose having been to a therapist or psychologist, and they might not have to (or maybe even be able to) tell someone who comes asking that you were a patient, much less see any private records. I'm almost certain someone would need a legal subpoena to get information like that unless your son signed a written release. You can talk to the therapist beforehand about privacy issues, and make sure you read any documents they want you or your son to sign thoroughly before signing them, to make sure he isn't signing away his privacy. If they refuse to give you a straight answer about your concerns about privacy, see someone else. You can also check with the insurance company what information about your coverage an employer would be able to see. I think you're protected, but I'm not positive. A legal advice line might have some info without you having to hire a lawyer.
Any legal types here who know more about privacy laws want to weigh in?
Yes they cannot make any kind of inquiries as regards a person's psychiatric record unless there is a specific legal reason why. In the meantime it would be worthwhle to find out about what other insurance options there are for now and for your son's future when he might not be covered under your insurance even with co pays.