Maybe this has already been ruled out, but I suppose that leads to the
simple possibility that Az/Diabetes are not especially linked(eg one
actually causes the other), but that in people with a damaged brain (damaged
by the accumulation of proteins that kills cells, aka Az), then further
stress on brain cells by starving them of glucose will "enhance" the
Alzheimers symptoms. And relieving the diabetes with drugs thus 'relieves'
the alzheimers.

Similar effect is seen with many of the AZ medicines which dont actually do
anything to target the cause of Az, just the secondary effect as we
understand it(lowered messenger chemicals).

Some of the press reports (and we all know how accurate the press can be)
seem to indicate much more of a direct causal link, as if there are
underlying connected causes, but perhaps as you say its really very simple,
Diabetes is simply exacerbating Az by weakening an already damaged brain.