Here's why I find the biggest fault with your argument. You say that no one will read the comics or watch the cartoon, yet they somehow have an understanding of what the JLA is. How? How do they know all this?
It's called pop culture. You just know these things. A reference here and a quick mention there give you a basic understanding of simple concept. Voila. How do people who've lived their whole lives without electricity (let alone TVs), people who can't even afford to glance at a comic, know who The Flash is? They just do. He's a pop culture icon, so he's bound to find his way into their heads and stay there.
Try doing this: Ask an average Joe, anyone who looks like they don't watch cartoons or read comics, to name the members of the Justice League. I assure you Spider-Man has more chances of being mentioned than Black Canary or even Hawkman. Why? Because he's a big superhero, and the simple, basic, elementary concept of the JLA is... yep, you guessed it.
