>"(If it were just a random coincidence, you would expect the plaques to show up in people without Alzheimer's, but they don't.)"

I don't see what "random coincidence" has to do with it, there can be a correlation for a pretty much infinite number of reasons besides the amyloid hypothesis.

Anyway this is wrong. It seems to be that ~20-30% of "cognitively normal" elderly have substantial plaques. This increase with age. The earliest reference I found for this info was 1937:

>"there is now building data on Aβ deposition in healthy controls that suggest at least 20% and perhaps as much as a third of healthy older adults show significant deposition."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844114/

>"An attempt was made to estimate the severity of the histologic alterations as a whole, and it was found that severe intellectual impairment was apt to occur in cases showing extensive involvement. However, this parellelism was neither close or constant. There were enough exceptions to make one reject the idea that there could be any simple and direct quantitative relationship between clinical and pathologic changes.

For example, in case 4 (Table i), a patient with a paranoid type of senile psychosis, there was only a minimal amount of intellectual impairment though the changes in the brain, particularly with respect to plaques, were very extensive."
https://ajp.psychiatryonline.org/doi/pdf/10.1176/ajp.93.4.75...

>"There is a close relationship between the degree of dementia measured during life and quantitative neuropathological changes found post mortem, with two important exceptions: (1) brains of nondemented elderly patients sometimes contain pathological features in a degree diagnostic of Alzheimer’s disease; and (2) conversely, there are occasional brains of demented subjects that do not contain markers of Alzheimer’s disease or of other disorders known to produce dementia that can be detected by neuropathological examination. The discovery of such exceptions led some neuropathologists in the 1950s to doubt the importance of Alzheimer brain changes as a cause of dementia in the elderly 1161."
https://www.ncbi.nlm.nih.gov/pubmed/2897823

>"Ten subjects whose functional and cognitive performance was in the upper quintile of the nursing home residents, as good as or better than the performance of the upper quintile of residents without brain pathology (control subjects), showed the pathological features of mild Alzheimer's disease, with many neocortical plaques. Plaque counts were 80% of those of demented patients with Alzheimer's disease."
https://www.ncbi.nlm.nih.gov/pubmed/2897823

>"Recent advances in amyloid imaging have made it possible to observe Aβ amyloid accumulation in the patient's brain. As a result, it has been found that there are many normal patients with amyloid deposits, and also AD patients with very few amyloid deposits (Edison et al., 2007; Li et al., 2008). Further, in the brain of elderly non-demented patients, the distribution of senile plaques is sometimes as extensive as that of dementia patients (Davis et al., 1999; Fagan et al., 2009; Price et al., 2009; Chetelat et al., 2013)."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5797629/