Well, that's a plausible reason behind it. A lot of people were just going "Zomg Rapture is an Alt Columbia!" without any reason behind it other than "JUST BECAUSE." Rapture happening in DeWitt-verse because Columbia is never built on that side by Comstock and the lack of his influence on history is possible. Though I still think both happening in the same universe is a
possibility.
Aso the Bathysphere thing is still a total red herring:
http://bioshock.wikia.com/wiki/Bathysphere
After Rapture society collapsed into Civil War, Andrew Ryan prohibited the use of bathyspheres by anyone outside of his inner circle.
It is revealed that Jack can use the bathyspheres only because his genetic signature is close enough to Ryan's that the security system doesn't deny him access. Sullivan clearly states this in one of his Audio Diaries "Sisters, cousins - anyone in the ballpark genetically will be able to come and go as they see fit."
So DeWitt either becomes part of Ryan's inner circle as an old man, is related to one of them, or is a cousin of Ryan somehow. Either that or they happened to pop in during the uprising and they had put warnings up that they were off-limits, but Ryan hadn't actually locked them to genetic markers yet (he does this just shortly before Jack arrives).