I was too lazy to find and read didn't have access to the actual study, but based on the article, I think they are sensationalizing and extending the conclusions a bit.
The crux of the study seems to be:
All had performed well on memory exams, although those whose autopsies showed Alzheimer's evidence had slightly lower scores on measures of episodic memory, which tested how well they recalled a story that had been recently read to them.
So, they took a bunch of older people, read them a little story about, say, soybeans, and later asked them questions about the soybeans ("What are some of the things you can make with soybeans?").
Later, when some of those people died, they sliced up their brains and found that the ones whose brains were in worse shape had "slightly lower scores" when it came to remembering about the soybeans.
Yes, it generally supports the idea that having a senior moment may be a sign of impending Alzheimer's, but from that to "If you forget having a recent conversation, you're just a few years from Alzheimer's" is a big stretch.
If that's true, then I know two teenagers who are headed for a care facility. Also, I can remember some significant senior moments that I had 10 years ago, and I'm still OK at 52.