That's probably playing with the exact definition of "detained". Rand Paul might be legally allowed to leave the airport and abandon hopes of ever flying commercial flights again so he isn't officially "detained".
I wonder if Rand tried to pull "I'm a Senator", or if he didn't mention that ahead of time and then let the TSA twist itself into a knot over how can they let him fly without appearing to give him any favoritism. I think the supervisor would love to give him one pat, let him go and hope the whole thing disappears. I believe the Paul family doesn't let go of things like that so easily, especially now that this has hit the public.
I believe that Rand likes to dress down (in street clothes and ball cap) when he travels, and so I doubt he did the "do you know who I am" routine, at least until after the TSA hauled him away to their private detention area at the airport. It's worth noting that he was apparently flying commercial like everyone else, rather than chartering a private flight, like say John Kerry.
Once you are in the secure zone you cannot leave without TSA permission. To leave without clearance is a crime.