Just be warned - this, despite appearing on the Nature website, is not actually a Nature article but from some other lesser publication they have started. It's certainly not a Nature quality article either - I remember being a bit befuddled when I read it until I found out that it wasn't actually what it appeared to be.
For a thesis like this it's always hard to know the direction of causality. AD brains are different, and it is at very least plausible that AD brains are more susceptible to fungal invasions.