Earlier quoted context omitted.
Saying "we apologize" multiple times is the same as "we're sorry". The difference is that the first indicates that "we" want you to feel better, while the second indicates empathy. When I'm on the receiving end, my gut reaction is almost exactly opposite. Second, their claim is that this is a miscommunication appears to be a CYA lie. The recipient has shared sufficient details of what actually happened that either he…
I maintain that "we apologize" and "we are sorry" are identical in meaning, except to those straining to be ungenerous, always demanding "just a bit more" prostration than was offered. Your compact "good apology" wording is fine, too! But if they'd used that, exactly, plenty of people would still be hair-splitting & demanding more – maybe even you, since even your wording doesn't do most of the things your first post…
The problem is that when you list your acknowledgements and chosen actions, you're implicitly refusing to acknowledge anything else and are indicating that no further actions will be taken.
When the apology is open-ended, and includes further specific actions such as an independent investigation, then you've done none of that.
The social function of apologies also requires gracious acceptance of actual admissions of error.
When the apology performs the social functions of apologies, it only works when the recipient graciously accepts.
But when the apology fails to perform the social functions of an apology, there is no obligation on the recipient to pretend acceptance.