Re his illness.
My take on this, firstly as a doctor; secondly as someone who has in the past received a potentially life-limiting serious diagnosis.
He clearly has "something", and the neurologists aren't sure what, but believe that it is something akin to one of the "parkinson's plus" diseases; he is however "fortunate" (inasmuch as receiving such a diagnosis can be) to have a mild and indolent case.
When people get serious diagnoses they often do go into a spiral. Things get misremembered and embellished; or they get ignored and downplayed. Note his consultant warning him off googling (end of first letter!)
Clearly TW has been relatively lucky in the course of his illness so far, and there's no reason for anyone to wish him any further illhealth.
But from a personal viewpoint, I can tell you the date I was admitted to hospital for urgent surgery, the date of my formal diagnosis. I know exactly which holiday I went on the previous summer, and which I did the following summer when I was still desperately trying to process things for myself. There's no chance whatsoever that I would misremember such a key fact. I'll bet everyone else here who has been in similar circumstances can say the same.
As someone else has said, jiggling the facts around so that the story is that he received a firm terminal diagnosis before they set off, propels this part of the story into fictional territory. I guess they still did the walk; it can't have been physically easy for either of them if he had as-yet-undiagnosed symptoms. But he had NOT received a terminal diagnosis, they weren't carrying the fear of early death with them, and whilst they may have been worrying about his symptoms, that's not the same at all.
(And before anyone says anything, I too was "fortunate" and, years later, (nearly) everything is fine!)