Completely ridiculous. How do they get away with this kind of stuff? I genuinely think the only way to put a stop to it is for an article like to get popular so they're forced to think.
I asked the rep if I could give any other form of identification, guess what - your email address on the 1and1 account would do. I tried sending them the html file from the same email as the one on my 1and1 account and they did what I requested. This boils down to - they really don't need your password.