A diagnosis of Alzheimers is a default diagnosis.   This means that they
rule out other possible causes and it leaves them with a diagnosis of
"probable" Alzheimers disease.

In my mother in law's case, they did a complete gerontological workup,
meaning that her thyroid was checked, a cat scan done, and then she went to
a psychiatrist who tested her too.  When all other possible known causes
were ruled out, then we were told it was Alzheimers, but of course, we
already pretty much knew that.

What your wife may have is usually termed "early onset Alzheimers" rather
than premature.