You have great, and completely misplaced, faith in BA human resources chaps! I'll speculate wildly here, but if it did happen to be the case that the Captain was clean, and it did happen to be the case that the FO missed his pick-up, and it did happen to be the case that the FO was obviously worse for wear, do you think BA would let the Captain who took him flying get away scot free? Not a hope in hell.They'll call that gross misconduct just for a start.
Why do you assume its fair to say BA had no grievance with this Captain? Do you know him? Those within the company say there's evidence that BA already did have a previous grievance with him. BA management have grievances with lots of people, and when they can't get them on technical breaches of the rule they criticise them for the entirely subjective crime of 'poor handling of the situation'. Its always happened, it's still happening and purportedly there was already one resignation in the pipeline from one disgusted Captain prior to this event.
BAs interest is to bury the story as quickly as possible, not to debunk the story. Did we see any official company rebuttal of the Dispatches program with its many fictitious claims? No. What we saw were people strung up by the company, including two guys who were actually sacked for no wrongdoing and later reinstated on appeal.
On the subject of false accusations, many people in BA are falsely accused of many things by their colleagues every year, from aclohol abuse to sexual harassament to racism to bullying to theft. I've personally known two people subjected to false allegations. They were stood down from flying, with associated loss of flying pay, whilst the allegations were investigated and found to be unfounded. Both accusers continued to fly and received no punishment.