I don’t know what the Heter for swimming “Untniuzdigerhiet”, but it might be because it is dangerous to swim with much clothing on, because you can get dragged down. But with regard to Excersise, I don’t see a safety issue for being dressed Tzniusdig, rather a convenience issue. So I don’t really get what this “Sensitivity” gibbirish is all about.
The Halacha is that even in private, you’re not allowed to be dressed inappropriatly, because the Shechina is all over.