Sorry for going OT a little bit, but is this the case with every airline, or only BA? And would it not have to do with the respective airports' staff in question, rather than the airlines involved?

Only because I was travelling ICN-TPE on CX in C last week, where at check-in they seemed to have "forgotten" to attach a "Priority" tag to my bag. After arriving at TPE, all other "Priority"-tagged bags definitely came out first, whereas I had to wait for mine 15 mins longer...

So at least on that occasion, they seem to have sorted them by pretty-coloured tag, and not by the barcoded one. But then I was flying CX, not BA...