In this case, in a proper study Alzheimer's had no business being mentioned at all. The only tenuous connection was that they share a common region of the brain affected. (here's the obligatory car analogy) That's like going out in the morning and finding a flat tire so you tell everyone you lost a wheel on the way to work (so they picture a highway drama involving a risk to life and limb).
The test group were diagnosed with "Cannabis use disorder". That is, not just average users, these patients were hard-core users who already were known to have problems thought to be related and refuse to cut back on use. It is thought that most people with that diagnosis had mental health issues before starting marijuana use. It would be interesting to see how their scans change if any of them can be convinced to reduce their use to more casual levels.
It would also be interesting to know how many (if any in the control group) were casual or occasional users. All we know from the freely available information is that they were not diagnosed with cannabis use disorder, meaning they might be non-users, casual users or even heavy users with no problems thought to be related to use.
As for legalization vs. recommendation, alcohol is perfectly legal and I think that's right and proper. Nevertheless, I don't think beer for breakfast is a good idea at all.