I've been following this news for a while now, and you're right a lot of people do not believe the statements that they've put out, and this is making a lot of them feeling uneasy.
You can't blame them to be honest, we're supposed to be in a decentralised space, and privacy is very important, if these guys cannot assure us of privacy then what's the point.
Like you said, just imagine if other exchanges do this as well, it would be a calamity, and I'm glad that since I've been using Bitget, I've not come across anything like this.