I'm pretty sure that translators who legally translate material have to get copyright permission, which means paying fees to the copyright holders. I know this holds true for music and printed works, so I'm sure it would hold true for films.
So, the possible reason for getting such a site shut down, was they were illegally providing subtitles, for which the said Association members had to pay fees for.
Would annoy me if I was in such an Association, I'm sure.
Cheers
Mick