Kinda illogical reasoning from Rory
Hundreds of Olympians compete for countries that they arent attached to for various reasons, he could have competed for himself, the sport or whatever. A half decent interviewer could have put that to him but I suspect that he hasn't really thought it through that much.
By trying to not being political he is ironically being political. Now he may feel no attachment to either flag or state or whatever that's fair enough but it isnt really a reason not to compete in a competition.
I suspect that the real reason was he didnt want to offend his mates and/or in his circle of friends its the vogue thing to be unattached to either flag and the more unattached you are the cooler you are so he's just going with that.