So, I read it:

1. It is not law. It was a proposed law that never made it out of committee.
2. There is no provision in the law regarding the results of that examination. Are the results of the examination to be made public? Is the standard we want that a candidate for president have his entire medical history laid bare for public examination? It's one thing to conduct the exam, but what is done with the results is critical - and unspecified.

Basically, it's a poorly thought out, poorly written law that would have been a legal nightmare if it had ever been signed into law. The biggest concern is: what if the candidate is deemed unfit to serve? Sleep Joe goes in for the exam and the doc says "Bruh, you're freaking senile"? What the law here has done is essentially add an unconstitutional test to become president that is not in the Constitution. Does the physician then to get to cancel the guy's candidacy? (unconstitutional) Does the party get to pick a different nominee or does this doc essentially create a one-man race if he finds something disqualifying?

And what if he doesn't find something disqualifying, but it's a bad deal. Candidate goes in and doc says "Hey Frank, I know you're a Roosevelt and sort of American royalty, but your blood pressure's sky high, you're about 3 seconds from a stroke, you can't walk, and you can barely stand long enough to give speeches." You shouldn't be anywhere near the Oval Office. It's not disqualifying, and let's say there's a giant world war going on and no one wants to look weak. Does this physician have a duty to disclose this information to the public? Does the candidate have any right to privacy? Does the exam constitute an unreasonable search of the person who has committed no crime but could potentially have his rights to run for office stripped by violating his 4th amendment rights to be secure against unwarranted search?

Like I said, it's a legal nightmare. No one thought this one through.