I'm going to have to respectfully disagree with you there. If you're having to research the history of the phrase, you're overthinking it. It means exactly what it states, no tricks. "Free speech" is a well known phrase that means the unencumbered ability to say what you like. "Free beer" means something that everyone (ostensibly) likes being handed out without the need for payment. I'm not sure how one could more simply explain the "free" dichotomy. If you've got a suggestion, I'm open to hearing it.

I felt stupid for the longest time with this phrase. Even after looking it up. Until I knew the history more I didn’t get it.

The confusion comes from the fact that beer generally isn’t, well, free!

There is no implication in the quote that beer is generally free, just that "free" in the context of beer generally means gratis whereas in the context of speech it does not.

Where do you live that beer is generally free? I want to go to there!