The Mayo clinic article you referenced specifically says that there is no risk from domestic air conditioners of Legionaires disease.
Errr, no, it doesn’t. It says
Although it’s possible to get Legionnaires’ disease from home plumbing, most outbreaks have occurred in large buildings, perhaps because complex systems allow the bacteria to grow and spread more easily. Also, home and car air conditioning units don’t use water for cooling.
It doesn’t “specifically” say there is no risk from domestic air-conditioning. It says it’s highly unlikely, partly because water is not used to cool the air. But there is water present in this instance (the whole point, really).
I said the risk is slight but real. I should probably have said there’s very, very little risk, but the Mayo article doesn’t “specifically” say there’s no risk.