"in the hotel"
As a native English speaker, if I ask someone "Are we in the same hotel?", I might ask this of someone who I think might be in a different room in the same hotel where I am located at the moment. I could imagine texting someone this, who I think is staying in another room. This kind of thing might happen at a big conference.
"at the hotel"
When I ask "Are we at the same hotel?", it would mean to me almost the same as saying "Are we staying at the same hotel?" I could ask it of someone while at a different location than the hotel.
Mapping "nello" automatically to "in the" is not correct.
Also the previous question:
Le ragazze sono nell'albergo.
Both of these answers are accepted:
The girls are at the hotel.
The girls are in the hotel.
So it is also inconsistent to accept "at the hotel" for "nello albergo" in one question, then reject it in another very similar question with "nello albergo".