What that is most important is to avoid giving your identity documents to people. Those sites too can misuse your identity documents that you submitted to them.
But if you do not give identity documents in these big websites or exchanges, they will put limit or restrictions on your account. Even to do P2P transactions on Binance, some sellers and buyers demand identity documents and they will deny the deal without these documents.
I think he meant about the other end that you're trading with, the other person but not the exchange. Although it's also true that these exchanges might misuse our identities and they'd say a guarantee that all of our data are safe with them. @OP, I've seen a lot of deals in Binance P2P transactions and just as what khaled said about following the guidelines, you'll have no problem. Because there were some cases that the other end is gonna try to rush you just for you to send him the payment without even verifying that they've already sent you what you're trading to them. Don't be in a hurry there because you'll never know the new tactics of fraudsters and scammers there but yeah, the platform is legit but it can be misused and abused by these cons.