The supposed relationship between aluminum and Alzheimer's Disease has been reported for over two decades. The original stories reported a link between aluminum cookware (pots and pans made of aluminum) and the horrible dementia disease. Like this report, the science was extremely sketchy. It was yet another study that asks a group of people a whole bunch of questions; follows their medical histories; and then at the end of the study, tries to correlate the answers on the questionnaires with any diseases contracted.
I could write a paper (actually I have written such a paper) on the massive problems with regression analysis, the mathematical tool used to try to find correlations between one of the answers given, and the eventual medical outcome. Bottom line: it is a tool that is almost guaranteed to produce wrong results.
Unfortunately, once the results of these studies is published, some part of the population believes it, and the story never completely goes away. Just look at the stories which link vaccinations with autism (which has been proven wrong many times) and see how many people still believe it, and act on it.
Like others who have responded in this thread, I'm getting a little old (Medicare starts this year), and have compiled my own life experiences. About the only ones of these thousand studies that I'm sure is true are the ones linking cigarette smoking to both cancer and heart disease. Those are true, for sure.
Finally, unless you cook every meal in aluminum foil, even if there is a danger (which I highly doubt), you'd never run into it by using aluminum foil because many of its uses, like covering a casserole dish, simply don't put the food in contact with the aluminum for long, and not at a very high temperature. If any problem was going to show up, it would be when using an aluminum pan for frying. I'm still here, despite the fact that when growing up in the 50s and 60s, our family used a small aluminum pan to pop popcorn in hot oil. Despite that, I still have most of my marbles.