I don't see how this would work to be honest. No customer - including those using the same TA - would be able to do anything with the OP's account. There is no such clause as "do not use the same TA as a bad person", and whilst of course, the "bad apple" theory might have potentially explained the temporary lock of the OP's account as superfluous caution and then would have led to the account being reopened intact, but it can't explain the conclusion that terms were breached by the OP's account, at least not in any way I can imagine.

To be honest, I think that even the idea of a bad customer with an above board TA is hard to conceive. I mean, if you are planning to do something dodgy with your FFP, the last thing you'd want would be to get the attention of a honest TA who would witness your manipulation and would risk telling on you, especially as they'd know that as third party nominee they would risk being suspected by BA if something wrong happened.

Call me too quick if you wish, but to me, unless it is a big mistake on the part of BA, the focus remains very much on the TA as the most likely source of the issue. Again, it seems that the OP are not entirely clear what "magic" the TA produced so we don't know exactly what they have done and there is a possibility they believed they were doing nothing wrong, but in terms of opportunity to do something wrong, it is either the TA or the OP really and as I precisely think all of us have chosen to take the OP's narrative at face value, it leaves only one option.