Naw, don't believe that at all. For one, it's easily true that today's gamers are as well read in fantasty (although likely different fantasy) than yesteryear's gamer. The idea that teens in the 80's were bigger readers than today is something I just don't buy. Given the ENORMOUS amount of fantasy available to today's new GM compared to someone starting in 1982, I highly, highly doubt there is really all that much difference.
I'm not talking about well read in fantasy, I'm talking about well read in general- RW mythology, religion, philosophy, the Classics...even non-fiction. You can tell by reading their products that Gygax & Crew read a LOT of different things, not just Howard, J.R.R.T., Moorcock & Vance. There are references to the Bible, history, pop-culture, sci-fi and more.
And I'm not singling out gamers- I think that this lack of breadth in reading is societal, and gamers (while better read than average people) just reflect that. I can't cite any actual evidence about modern readership, of course, just personal anecdotes.
When I was in law school, for instance, the fact that I read anything besides the newspaper & textbooks came as a surprise to my classmates. Our profs were much more broadly read, and I often found myself explaining classical references (such as "Sword of Damocles") to classmates in study sessions.
Among the gamers in my overall social group, the
only ones who DM are the ones who read more than a few books a year.
Part of that reading/DMing link isn't just about what you read, but also about the patience and time it takes to go through a 700pg novel or a 300pg history book, etc....which translates into the patience for the bookkeeping of the DM's job.