Yep, the OP was much more polite than I would have been.
Let's see. My 10 y/o goes in the men's room by himself, but when he started depends on where we were. Someplace small and familiar, he was probably 6. Someplace larger and not familiar, I still hover the door. We try to use the family restrooms when possible, and DH goes with him if he's there.
My 8 y/o is autistic so imho the rules do not apply. He does not go by himself, because he still has trouble handling buttons and zippers, and is fascinated by automatic-eye sinks. I have let him go in with older DS a few times, if it was a restroom that was basically unoccupied and I could stand at the door yelling thru the crack.

But seriously, I do this whole routine when I take him in the bathroom, I talk to him, and if anyone has ears they'd figure out he was in with me because he needs assistance.
I do remember once a few years ago, I let older DS go in the Wal-Mart back bathroom by himself, because it was empty. I was hovering the door and a guy went in there. A few minutes later the guy gets done (I guess) comes out, and I asked him if my son was still in there. (a silly question, in retrospect, as there is only one door) He looked back in and said yep, he's playing in the sink, and held the door open for me so I could tell DS to
quit playing and get out.