For the purposes of this question, lets go back a few decades to before your IRS started getting pushy about finding details of secret bank accounts, if in fact that makes any different to my question.
You often hear (at least I have ) about rich people, particularly those who got their riches through less than angelic means, having their money stashed away in secret Swiss bank accounts. Did the Swiss banks go so far as to completely refuse to acknowledge the existence of a client if that client forgot their account number? If someone else managed to find out their account number was that all they needed to drain the account? Basically, how did such accounts work?
Yeah, this. Part of why it was tolerated for so long was that you (or more commonly your intermediaries) actually had to to a lot of legwork to open and maintain an account in a financial haven. It was expensive and not really an option for the rank-and-file of the criminal world. Once it became practical to open a hush-hush account doing most of the work electronically is when it became a problem for most of the world’s governments.