Since Riker read out and confirmed
Yamato's registry as 1305-E and not being called wrong by anyone on the bridge, confirms the registry. It would seem that we're just having trouble accepting that other ships in the fleet can have an exciting life
I don't understand this argument. He didn't confirm anything. He just read it out from the hull. The fact that no one bothered to double check on their computers in a stressful situation is not a proof. In fact, they are not even checking their computers, they are just looking at the screen. Geordie is the only one working, and he's at the engineering station.