this is seriously restrictive to anyone wanting to get into bitcoin, like its meant to be pseudonymous but if the gate ways into bitcoin dont allow that people will be put off.
You need to get mad on this things or you don't have to worry because it is very normal for the exchange platform to get the information of their client for the security purposes only. And you have 2 option that you can do 1st follow what they want you to do or don't follow their rules restriction on buying bitcoin.
This way you can never be traced since government or any one never doubts these payment processors and hence its quite simple. That advice he gave me is yet very useful and one that I personally follow.