Although every case does not happen like this often the film media network contacts the ISP of the host sharing the copyrighted material. The ISP then takes steps to contact the user on it's system to remove the copyrighted material. So in this case the ISP would make contact with you on behalf of the media company.

I would take the case you have seriously but be careful who you're dealing with. You wouldn't want to give out information to some spamming party.