From the article:
"The NFL has for years gotten complaints from draft prospects about the length of time for medical examinations as well as the redundancy of having doctors from all teams examine the same player and ask the same (or similar) questions."
That actually seems like a legitimate complaint. It seems like there could be an independent medical evaluation done and provided to the teams for their review. If you want more in-depth medicals from your own doctors, bring the player in for a formal visit.
We don't ask them to do any of the other testing 32 times, once for each team.