He didn't say they could fire on the move, you have misinterpreted him. He was replying to your denial of his statement about "LMG cancer".
So his statement "Have you seen 1919s on paras and riflemen" doesn't mean "they can shoot on the move" it means "they are (in his opinion) a real pain and spoil gameplay".
I hope I cleared that up. I think you're probably auto-disagreeing with what he says. I'm not saying he's right but if you want to have a constructive discussion with him, you'll have to at least understand and take on what he writes before writing "you're wrong".
He was responding to me about firing LMGs on the move