No, of course you're right, the "toy model" is exaggerated. I think it was more true in some countries than others and several decades ago, when there was no internet and the media were dominated by a few players (including the government itself, in many countries) all very much established.
Let's say that I suspect that democracy is a system that assumes public opinion to be directed so that it doesn't stray too much from a narrow range of possibilities. This can be done just by manipulating the Overton window.