Aren't you missing the point by blaming the IT systems? Would I be right in thinking that in the example given, at some point someone somewhere has input stand TA3 instead of TA4 into the system? In many ways the fact that it was an IT system is irrelevant, as it could have been hand written on a piece of paper.
The problem is that the managers of the tug drivers have hammered home to them (bullied?) that any deviation from the instructions they are given will result in a b*llocking, which the tug drivers naturally wish to avoid. The problem can only be solved by someone with the authority to change the stand in the system Chinooker's manager it seems), which then results in a revised instruction to the crew, which they are then happy to carry out.
As has been said previously the management method generally in BA seems to be to robotize their workers as far as possible, which is probably why as soon as anything unusual happens (fog, snow, T5 etc) the whole thing falls apart, because those lower down the food chain aren't allowed to improvise.
Having read Gordon Bethune's book 'From Worst to First' it all sounds very similar to the dark days at Continental that he was instrumental in overturning - perhaps the BA board ought to give him a call and see what he is doing these days!
Things will never be perfect at a large company, as you will never get perfect top-to-bottom communication, but there are ways of making it a lot better than it seems to be in BA at present.