Ah, that's actually simple - the answer depends on whether that statement is true or not.
In the abovementioned case where only name (which is not unique) and password and sexual orientation is stored, and literally nothing else, you can say "sorry, we took all reasonable measures to verify your identity, and couldn't" because that's how it is.
However, if google or paypal or someone else who stores much more data says "sorry, there's no longer any way for us to verify you are who you say you are", then that's a lie (easily verifiable by the regulator), and that's not acceptable.
In the abovementioned case where only name (which is not unique) and password and sexual orientation is stored, and literally nothing else, you can say "sorry, we took all reasonable measures to verify your identity, and couldn't" because that's how it is.
However, if google or paypal or someone else who stores much more data says "sorry, there's no longer any way for us to verify you are who you say you are", then that's a lie (easily verifiable by the regulator), and that's not acceptable.