In the words of one popular meme, "I don't always drink beer... So you probably shouldn't consider my opinion of it authoritative." Also, why exactly does a beverage have the slogan "Stay thirsty"?
The point being that he's so badass and refined that he obviously has excellent taste, and the one beer he drinks is bound to be incredible. If you're thirsty, you drink. If you're still thirsty, you drink some more.
If you drink beer, it's probably not the only alcoholic beverage you drink, right? He would be less interesting if his preferences were narrow — he's obviously the sort of person who'll drink liquor or wine if the situation calls for it. It's not that he doesn't like beer, it's just not all he drinks. Plus, trying different things lets you have a more authoritative opinion, doesn't it? Like, out of all the things he has tried, Dos Equis compares favorably. Also, I think they wanted to portray him as not excessively enthusiastic about Dos Equis, so he'd come across as a cool person who's not excessively enthusiastic about things.
The "stay thirsty" part seems more about continuing to have a thirst for adventure like him, and so cultivate a long list of stories and adventures to share with the people one meets over a beer or whatever drink one prefers.