This thread is revealing as to what can happen when your info leaks -
https://bitcointalk.org/index.php?topic=5166119.msg51886832#msg51886832ICOs hiring 3rd parties to conduct KYC so I don't think there is anything to worry about.
I've come across plenty of third parties who looked no more or less impressive than the shittest ICOs. I was directed to one 'professional' service that did the verification through an app. On checking it on the play store it had been downloaded 100 times. That's not going to persuade me to trust them.