Confirmed: The news from Nikkei was not false. And Binance is responding:
https://cointelegraph.com/news/major-crypto-exchange-binance-to-open-office-in-malta-after-japanese-regulator-warning

@gentlemand - I don't know why most would not save their private key. This is a lesson that has been drilled upon since dawn of bitcoin. It is very very important. And with electronic failures, it is important to make a physical copy. - And with passwords, there is no "Click here if you forgot your password" button on a private key.

If you are just toying with trivial amounts, it might not be a big deal to have backups, but anyone serious about keeping anything of value needs to follow the standard procedure.