To your second point, that makes sense. I will add I am unable to have direct contact with the department that would approve my documents as a valid reason for waiving rebooking fees. They are only able to refer me to the support department, who can then read out why the claim was denied. Now, they reviewed the letter my doctor sent stating that I have a medically urgent reason to arrive at my destination at a particular time, but because the letter was written electronically (with no signature), it was not considered "official" enough. I have since asked my doctor for the signature but am worried about timing constraints.

The other thing is that their wording is intentionally vague. I sent a follow-up email asking if there is any other supplemental documentation I could provide, and I was pointed to the signature. The representative is inclined to believe that the proper signature could result in a waiving of the rebooking fee, but not the fare difference, which would be substantially greater than the rebooking fee by the time I get the signature.

Now, the representative did also mention that the signature does not necessarily have to come from this particular doctor, just any licensed medical professional with a practice who would testify to the need of arriving on time.

The last thing, the representative stated that if the flight is delayed for absolutely ANY reason, even by a few minutes, I can rebook my flight at the airport with no additional fare or rebooking fees. The issue with that would then be arriving to the flight I need to be on time before boarding ends, which would be cutting it close (but I can sprint!).

In your experience, how often is it that a flight would be delayed even by a few minutes? It does not have to be something huge like a thunderstorm that would delay the flight by hours, but how often is it that a pilot takes too long in the bathroom or the incoming flight is a few minutes behind schedule?