May I ask you where did you get the info that binance is supporting ETZ?
I just went to their official website and find some info about the fork. I just learned that binance has not yet announced their support to ETZ. Yes, I transferred my eth to binance and I'm not sure if I can get some ETZ. My fault for not having some research first. I should have left it in my coinomi, if I know.
I found out on Binance's twitter account but did not find the info, seems like hoax. I just found the info on the Etherzero website that they listed Binance
https://etherzero.org/index.html?id=2#ExchangesI ask someone from the Ethzero telegram about the listing of ETZ to binance and I got an answer from (I think) the admin. Binance has not yet announced or confirmed to list it as per his answer.
Maybe Mazt rhiezt is right, this is just to attract investors.