Drafting BPA gives you flexibility in the future. If you suddenly have a wealth of talent at a position, teams will be willing to give you good compensation for backup players. Then there is the obvious benefit of having a very talented replacement should the starter go down with an injury. On top of that, should when your other starters are looking for big paychecks (Brees), you still have a capable backup waiting in the wings (Rivers). I'm not saying that the organization did a good job handling the situation, but they at least had a talented player waiting to take over. The same could be said with Denver last year, Jake Plummer was coming off a career year when they drafted Cutler, look how that turned out for them.
If the team has two players ranked very closely, then go with the guy that fills a need, but if there is a pretty big talent differential, go with the more talented player. It generally works out better in the long run.