Its not a requirement.
it's not only
not a requirement, but it's a stupid concept.
Why put a firearm you cleared and checked on safe -- assuming you even can? There's no reason to. So what if someone pulls the trigger? It should be re-checked and pointed in a safe direction if they do that.
The entire interaction sounds like someone trying to throw his weight around and sound authoritative when he had nothing better to do.
He should have asked the passenger to verify the weapon was unloaded and cleared and never touched it himself. if something were to happen to break at that moment, TSA would be paying for repairs/parts. Last one to touch it broke it.
Many discussions here warn to never let anyone, especially airline staff and TSA, handle your firearms. Tell them you'll show them anything they want, but you'll be the one doing the handling. Regardless, it's bad policy to allow anyone other than the owner handle weapons. What if the thing really did have a round accidentally left in the chamber, and the TSA agent causes an ND?