While I can't quote any specific law (or more likely, regulation), it makes sense under normal circumstances. Certain items have to be packed in checked bags so that the passenger doesn't have access to them within the "sterile environment" beyond security. Obviously, allowing a passenger access to their checked bag while within the "sterile environment" at a connecting point would also allow access to any of these items they might have packed - a no-no.

While what you were told probably is the "letter of the law", allowing you to pick up your bag at baggage claim and recheck it the next morning at the ticket counter would keep the spirit of the law. It would merely mean that someone would have to track down your bag (still in AC's possession or already transfered to UA?) and deliver it to baggage claim.

Of course, you were asking a GA for access to your bag while within the "sterile environment", so that may have prompted the reply.

Jim