The reality is, is that the NFL baseline testing is likely a joke. It's a cognitive test that players have to do with individual results. To really play devils advocate, you could even ask, are players taking these cognitive tests and acting like the biggest idiot in the world so if they ever get a concussion, they can easily clear it?
From what I was listening to on the radio earlier, these "independent evaluators" are actually employed by the teams. That's what happened with Tua when he had his "back spasms".
Either way, players are going to want to play even if they had their "bell rung" because they have that competitive nature in them so if the doctor tells them they are good they are likely going to say "well the doctor said so, so I guess I'm good".