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.
Are you so sure? I would argue that they would be extra vigilant
since right before that they were fighting an imaginary Romulan Warbird.
What we see in the episode, is Riker walking forward toward the magnified image of the Yamato. As Timo points out, he would have available to him far more resolution than we would, even if we were looking at the HD version of the screen.
Then, we also have Data running a full scan on the Yamato after he hails it.
At no point does any crew member go, "Hey wait a minute, the Yamato's registry is wrong!" They suspect the ship is an illusion because of the Warbird, but they do not suspect the registry is wrong.
So, I'd argue that not only were the computers double-checked, they even performed a full scan of the Yamato.
WORF: Captain, there's another vessel approaching in sector zero nine one, mark two six.
PICARD: On screen. Magnify.
RIKER: It's a Federation ship. NCC one three zero five dash E. It's the Yamato, our sister ship.
WESLEY: The Yamato's nowhere near this quadrant.
PICARD: Open a hailing frequency, Data.
DATA: USS Enterprise to USS Yamato. Respond, please. USS Enterprise calling USS Yamato. Respond, please, on this frequency. No response, Captain.
PICARD: Make a full scan.
DATA: Life support system, engineering and propulsion all appear functional. But there are no life signs, sir.
PICARD: Data, can we be getting a false reading?
DATA: Since we know nothing of these circumstances, it is at least conceivable, sir.