I honestly don't believe Joe has Alzheimers; his recent memory seems somewhat intact, with a few glitches now and then.
I believe he honestly has some kind of dementia but not Alzheimer's ; that would be to hard to cover up, and would be very noticeable even to people not familiar with Alzheimers. - Tom
Joe probably has common garden variety senile dementia, similar to my Mom, except my Mom is 91 years old. Typical symptoms include loss of memory, especially short term memory, both of which lead to a steady state of confusion.
Also, old people with dementia don’t think they have it, and they regularly deny that anything important has changed with their cognitive abilities.