Mintflavour,
I am neither BA nor a cadet. You are right to say that you feel confident of making a good pilot despite having twice failed BA entry tests. Good luck to you.
However, I would say that the BA selection process does generally weed out the good from the bad and even the very good from the good. Competition is fierce as you well know and being the best sponsorship around attracts people who are practically and academically very sharp. There are bound to be exceptions, but I reckon they are very few and far between. I am sure people in the know will confirm or deny what I say.