What we call "Alzheimer's" is probably a variety of disparate processes that lead, over time, to brain failure. The most common of these processes is probably above average aging of the brain. In other words, "Alzheimer's" is what you find in aged brains, it's where we're all going. Some get it sooner, others later.
Those whose brains age faster, or who start with less capacity, get demented sooner. Since accelerated aging seems to be inversely associated with malignancy risk, those who get demented earlier are less likely to get cancer.