It must be a nightmare keeping all that balanced.

It's all mathematically sound when you just let users trade with each other.
A person can't sell a token they don't own.
Every token sold on the exchange was deposited into the exchange's wallet.

At this point Binance has been so utterly captured by American regulators that it's actually irrational to assume they can get away with all the crazy shit they were pulling back in the day. Maybe they're doing new crazy shit by making deals with the politicians that captured them. Who knows.