Alzheimer's boils down to cellular regeneration but the root causes of it are genetic. If it were some extrenal thing the body could fight off, maybe a wizard would be "immune" to it. But if it is something they are born with it would still effect them eventually. If the body is making defective cells because the genes are telling it to do so, thems the breaks.
However we dont understand the disease all that well. It is clear that damage to the brain from things like head trauma can accelerate or even possibly be the cause of it in some cases. So if it was caused by that, the wizards would have much more insulation from the effects.
Honestly, Jim has a ton of leeway in how it works, because of how little we understand about the disease and poor understanding of the human brain in general. In this case, it is very easy for it to just be whatever he says goes and it will still make perfect sense. So to that end, we know from WoJ that Wizards CAN get it (and related things like dementia) but likely will get it much later and slower. And that fits just fine with the story.