Captivep did, I agree. And that is the level of discussion I was hoping for. Yes, I learned my lesson and I have to admit we didn't even think about these issues before. The only thing is I did not call without any information wanting to know whereabouts of person X (har har, evil lough) - then I wouldn't even be posting here. But I had name, date of birth, name of accompanying person, ticket number and record locator - so I had some information that not everyone was privy to but only persons with access to that information, e.g. the parent.
In any case, I guess I might have been less touchy if the handling BA staff would have been a bit more understanding and friendly and maybe explaining then my frustration would have been considerably less. The AA person tried with the same result of course as she referred at the end to BA - but the impression left was for me that I am not using BA again and that AA customer service was in contrast to BA really good.
Maybe we can agree that the one thing BA should have done differently in this case is the way how they are dealing with a customer who has an issue and is frustrated.