Shouldn't the GM have access to the chat logs, among other things? I can't imagine it being too difficult to skim the chat logs, see that the individual joined, said "hi," raided the FC chest and then immediately left. I'd imagine they'd also be be able check on the chat log of the FC that the individual immediately went to, for further evidence of wrongdoing. They keep track of everything else in this game, I'd assume keeping track of chat logs would be given. Perhaps I assume too much?
I'd also like to point out that the Lodestone website is such a lovely tool for these thieves to use. I just did a quick search for a mid sized FC, with recruitment open, and has an estate built. Coincidentally, our FC was first on the list, and the person that did the inviting was contacted right out of nowhere. I'd have to wonder if other FCs on the list had been contacted. Stealing is allowed in this game, so it's quite possible that they've done this more than once. I may be assuming too much, but it is quite an interesting theory. I'd be curious how many times one individual could get away with stealing from FCs, before the devs begin to take notice.