They detained him because he was traveling with stolen national security documents. He was acting as a courier between Greenwald and his partner in Berlin. His trip was paid for by the Guardian.

He was detained under a terrorism law because the leaked NSA programs (whatever their faults and transgressions) are nominally aimed at fighting terrorism. So, under what you admit is a very broad law aimed at fighting terrorism, this courier of stolen documents was stopped and those documents, which the UK and US govts (rightly or wrongly) think can aid terrorism by revealing to terrorists how we track them, were taken from the courier.

And that is why Glenn Greenwald's partner, who Greenwald intentionally and knowingly used as a paid courier of stolen national security documents across international borders, was detained and any media which might contain secret documents was seized.