It doesnt quite imply democracy does not work. It implies that propaganda works. And if propaganda works, then that would mean that having the bulk of the ability to propagandize concentrated in a few hands in a threat to democracy, as it means that few people effectively have a much more powerful vote. Which, if you'll allow me to shortcut the rest of the argument, just brings us to the fundamental threat to democracy is concentrated wealth and concentrated power.
It doesn't require concentrated wealth, but if wealth is evenly distributed, then presumably the power to apply propaganda is also equally distributed. Propagandizing information effectively become a meta-level form of voting. With concentrated wealth and power, those with all of the resources hold all of these meta-level votes.