Just because factory "books" says it's available doesn't necessarily mean it was so. Take the 1970 Corvette, Chevy lit says LS6 was an option and every Corvette guru knows that didn't happen, in fact there is no disagreement that the LS6 never made it into a Vet in 1970.There's lots of things in Chevy books that never happened.
True, that can sometimes happen. Just like Bucket Seats in '61's. There are some factory photos of them, but it didn't happen. But I had learned a long time ago that this was different. Did you read Tommy's post? I believe Verne Frantz also agreed. Whether one was ever made or not is not the issue. But I do believe, if you wanted one in any Impala, you could have ordered it and they would had got one delivered to the dealership for you.
Now, as mentioned, it not my obligation to prove anything. But I would say that it is not impossible that one in a non-2-Dr HT or Conv was ever made. The car is now 62 years old. A good percentage of '61's were wrecked and junked in the first 5 years alone. Who knows?
There are also a few other stories out there. As an old Nomad owner and fan , we always believed that there was only 1 '54 Nomad ever made. But not that long ago someone produced about 4 more hidden somewhere. I'm not saying that's true either, but it sounded so. As just one example anyway.