The study was not a double-blind, placebo trial which means the positive result could have been because one of the following:

1. Patients didn't actually have Alzheimer's. Given the only definitive test for it is a brain exam after death, this is possible.

2. There was a placebo effect.

3. There was a therapeutic effect better than placebo.

You are assuming #3 but we can't draw that conclusion yet. Even the authors of the study aren't claiming #3.