Weird choice to only let user who login can see the contact information. If i were freebitco.in user who barely know about bitcointalk & can't login, i would use social media since that's all i could found.
I think you're right, contact form just logged in users probably isn't best decision. As I said, they have support email, but it's not listed anywhere on website or social media accounts, so, most users probably have no idea that it exists. I believe that many try to contact them via social media. But it's managed by PR agency, so they won't get help there.