I'm not sure why you think it's strange, but maybe the term "private identifier" is creating confusion.

Your username uniquely identifies your account, but it should be kept private because it's also used for login. You don't want to share your login credentials with anybody. The public account ID also uniquely identifies your account, but it can't be used for login. So it's safer to share publicly. Still, it's probably best not to share your public account ID if it isn't necessary (just share your ticket number instead).

Any Kraken staff on this forum or any other public space should only ask for your ticket number and maybe your public account ID if appropriate. If you are asked for your username, email associated with your Kraken account, or any other sensitive information, you should be immediately suspicious and not give it out.