From the department of stating the bleedin' obvious
Facebook is an American company.
America has the Patriot Act, which effectively says that plod over there can shout "Terrorists!" then march in and seize data from any American company they so choose, with hardly a murmur.
So, if a person's Facebook record is of such amazing interest, the simple option for our idiot cousins over the water would be to ask the incoming suspect their name, then go over to Facebook, back their database up to that of the NSA and then simply grep through for info on that particular Facebook user.
Simple indeed, and not done because this trawl has been dreamed up by lackwitted goons in the ports, not in the American executive or legal hierarchy.