No, they’re not full of shit. We understand you may legally purchase from a private seller, and there are other means of getting ammo.
The problem here is with the business not allowing persons otherwise in compliance with the law from shooting on their range. They have the right to deny you if they choose just because they can.
They follow the rule that one must be 21 years of age to rent on the range, or anyone under 21 years of age be accompanied by someone that is of age.
They have to cover their liability and if you have an issue with that seek to address this loophole through legal means. Otherwise, go shoot in the state park, or on private land.
The caveat is that when I was younger, and shot at one local range, I befriended the owner, and made it clear that I would always bring all my ammo with me. He chose to allow me to shoot because I was able to convince him of my upstanding credentials. He asked only once to watch and after that I was allowed to shoot which I did at least once every other week.
If the owner doesn’t see the issue with the laws in this circumstance then there no friend of the shooting sports and I’d take my business to another area.