I sympathise with that point - I think it would be good if airlines gave more details about what breaches they assert people have committed, but unfortunately, my impression is that no airline (BA or otherwise) does that. As for "making this right", well, again, the assumption you are making here is that your TA didn't breach the rules, but until and unless you speak to them and ask them what they did specifically, you won't know that. Whether they "intended" to breach the rules or were conscious of doing so is another issue, but unfortunately, in cases of alleged fraud/misuse, whilst bad intentions do make things worse, good intentions are never enough to exonerate one in case something was not done rght.

Ultimately, having a third party nominee is a bit like giving the keys to your flat to a friend or someone else. You hope that they will behave, but if the neighbours below claim that your friend did something they shouldn't like flooding their flat or making huge noise at night, they will turn on you, not on your friends, and whilst they may give you a very generic sense of what went wrong, it's probably best to get the friend's version of what happened anyway if you want to figure out whether the property managers are being unfair/heavy-handed or have legitimate cause of concern. The fact that you think your friends are good people is no longer really relevant. Of course you think so otherwise you wouldn't have given them the keys to your flat in the first place, but now, your neighbours are clearly complaining that they were not and you can't just rely on the fact that you know they are good people in general and you can't imagine them meaning any harm. At this stage, it has and can only be about the specifics.