They are correct - but you didn't ask the right question. You want to ask for a day room rate - where you don't stay overnight. The last time I checked, which was about six months ago, they did. If , for some reason, they don't anymore, call the Comfort Suites - they are cheaper anyway and have full amemities at the Atlantis.
If all you want to do is go to the beach - just go to the beach. All beaches in Nassau are public - even the one in front of the Atlantis. The water attractions at Atlantis are the water parks - some of the best in the world.
I think you'll find the comfort suites rate around $110 - for a family of four, thats not bad.
I don't have a problem finding a public beach on Paradise Island but the information ascertained from a Nassau web site states emphatically that there are no public restrooms at any of the public beaches and you MUST spend money at one of the bars on the beach in order to use their restrooms. I'm traveling with my grandson and close proximity to a public restroom is a high priority, I don't want to have to bring him to a bar in order to use a restroom.
OK - last tip. The hotel next to the Atlantis has changed management since we were there - it was a Marriott then. We walked around behind to the beach, found the pool boy for the hotel, slipped him $25 and for that we got beach chairs, hotel towels and the use of their clothes changing facilities, rest rooms, showers and the outdoor pool.
We just got back from Nassau on 7/1. We were on the Sovereign and were docked from 7:00 am till midnight. I booked a room ahead of time at Atlantis just as though we would be staying 1 night. It wasn't much more than the Comfort. Just remember Atlantis is a huge place and I didn't even see the comfort inn. I assume you would have to walk a pretty good distance. You can book a day room at Atlantis but only if they have one available the day of arrival. When we were there there were no day rooms available and I was glad we booked early. By booking the way we did, we were able to stay late. I was told if you book a day room you have to leave by 6:00. I would definately do the same again.