The draft is almost entirely a subjective process. As Pat Kirwan says, it's like a beauty contest and beauty is in the eye of the beholder. Accordingly, he also says that draft boards are like finger prints...no 2 are a like. So there is no such thing as a universal BPA because teams rate players differently. If you surveyed every team as each pick was being made as to who the BPA was you'd get many different answers. Sure, at the very top of the draft there may be general agreement on player, but once you're out of the top 5-10 the divergence of opinion gets wider and wider.
The best drafting teams do the best job rating the players for their particular team and then stacking their board accordingly. Then during the draft they stick to their boards, taking the BPA for them at each pick. Also, the further you get down in the draft the more likely you'll have multiple players rated about the same. That's where need can really come into the process. If you have players rated evenly, go with your greatest need. Where teams get in trouble is where they take lower rated players over higher rated ones due to need.
All that being said, going with your BPA doesn't always guarantee success because going into every draft we know that the large majority of players drafted will never pan out. That's true every year. So all the labels that are spewed during and right after the draft mean nothing... BPA, Steal, Reach, Bargain, etc. You look back in a few years and you see how many of the labels were completely wrong.