Or are they competing hypotheses?
reported here in January: https://news.ycombinator.com/item?id=18987015
Age when teeth are pulled probably correlates well with age when Alzheimer's is first noticed.
It's like "newspapers cause cigarette addiction, people always buy cigarettes in stores where they sell newspapers" [apparent correlation; insufficient observation].
There was another HN thread about the "indestructibility" of prions, and I believe there is a growing consensus that they are not removed by existing techniques within dentistry.
If #2 then I'd venture to say that in many / most cases that correlates with abuse of sweets (read: sugar) which would all effect the teeth (and perhaps in turn the gums).
It's unlikely that simple. That said , I'd venture to say aggregate increase in sugar consumption correlates to increases in Alzheimer's. Yes, as do plenty of other mod cons.