They're politicians - they don't need evidence or science. They can just spout whatever BS gets them votes, and the general public doesn't care enough to spend five minutes looking into their garbage.
About dolls, I've never seen the appeal - but it generally seems like a hard thing to research, whether it's legal or not in a specific jurisdiction. I've read of a few cases of people getting into trouble - including prison time, which is pretty insane.
Australia, in particular, seems to have a problem with them: