Medicine is part art and part science. There is no way to establish a firm objective criteria as to whether an injury prevents a guy from playing football. This Michael Roberts waiver claim and failed physical is a clear example.
New England voided the Roberts trade with Detroit based on a failed physical. That's one medical opinion. The condition of the trade was that he must pass New England's physical. The Packers evidently thought it worth their while to render their own second medical opinion. As it turns out, the Packer physician came to the same conclusion as New England's, though it is entirely possible the guy had multiple issues and the two teams ruled him out for different reasons.
It's no different than if you had an ailment or inury and sought two medical opinions. You could get two different diagnoses, prognoses and treatment plans. This is kind of obvious.
In the NFL, there are situations where the medical opinion matters and can be disputed.
For example, there could be a dispute over the amount of an injury settlement with an non-vested player. That settlement is dependent on the number of weeks the injury would disable a player. The player may believe the team is understating the severity of the injury and the amount of settlement with the matter ending up in arbitration.
Or a player may have a contract guaranteed for injury. With shoes on opposite feet, a team might want to release an injured player for unrelated performance/cost issues and seek to make a case for not paying that player the injury guarantee in rendering a non-disabling diagnosis. The player might wish to argue Once otherwise, that the injury is far more serious than the team doctor assessed. Once again, on to arbitration.
What I don't know is whether Roberts failing a Packer physical voids the waiver claim and any contractual liability incurred in claiming him. Given the kind of player Roberts is, a 4th. rounder on a rookie contract being claimed, it might not matter whether the claim is voided or they had passed him, kept him for a week, and then cut him.
Whether waiver claims might be simply voided upon physical examination might be elucidated in the CBA, Article 29, "Waivers", page 155 or in some other spot in this document. However, my interest in the subject given the instance of Michael Roberts, is already past exhausted. You can explore the matter further here:
https://nfllabor.files.wordpress.com/2010/01/collective-bargaining-agreement-2011-2020.pdf