I wouldn't pretend to have a very well informed opinion; I retired a few years ago, I've never been a neurologist, and I don't remember ever meeting a patient with CBS/CBD. (Parkinson's, yes, and other parkinson-like diseases).
But my vaguely-medically informed opinion is that TW has an atypical form of something along those lines. I see nothing to dispute the idea that "something" is going on. (We've seen mention of a scan showing depleted dopamine levels in the brain). Parkinson's disease has been recognised for over 200 years but the other similar syndromes are more newly recognised and I suspect there's still a lot of research and learning that needs to be done to understand them better. However atypical presentations of all sorts of illnesses are actually quite common.
If you have a relatively unusual illness, then a rare presentation of it, of course will potentially cause a lot of uncertainty and confusion.
So SW may well be correct in her rebuttal; he has a neurological illness. But it's certainly not running the usual course and my personal opinion is that the WalkerWinns have been wrong to make out that he's at death's door with this.
However I also understand that when you get a potentially serious diagnosis, your mind can definitely leap to the worst possible scenario and so she may be totally truthful in how scared she and TW were at the idea of CBS.
I think that any serious illness, especially one where there is little active treatment but a poor outlook, can make a person feel totally out of control. The idea that you can regain some control somehow is very attractive. Hence the frantic hunt for unlikely "cures" that you see many people doing. In the WalkerWinn's case, that "cure" is the physical exertion. Someone with a typical Parkinson's-like disease would be getting streadily worse and be unable to do these long walks; but TWs illness is atypical so maybe the benefits he gets from extreme exercise do help his symptoms. (Also of course, serious physical illness can make you feel depressed; depression can make you slow down; exercise, or taking an active control can make you feel less depressed; and improving your mental health will make you feel more generally better).
I can't explain or understand the discrepancy between scans that she reports (ie that the walk normalised a previous abnormal scan). In my view either she's lying; or hearing/seeing what she wants to hear/see; or the scan has been wrongly reported. I'm not in a position to comment on which of these is the likeliest!
And I haven't read TSP for about 6 years so I can't comment on specifics in the book coz I don't remember them!