AFROTC will require you to go to a DoDMERB doc. That doc maybe your family doc, but unlikely. If you are military you can use the base, if not than they will send you to theirs. The only time you will go to a military doc is if you decide to go rated (fly). This will be done the summer of your rising 400 year, they will send you to WPAFB for a 3 day physical.
One big reason they don't send non-scholarship cadets for an exam is because it is only valid for two years, thus if they send you the summer before your freshmen year, but you don't contract until your junior year, the exam is not current. IOWS, it would cost them more money requiring an exam without a scholarship.