Are peeps gullible enough to believe one fake news? Prolly not. But then this misses the points. The hard part to understand is plurality. It's not just one story that convinces people.
Make a lie simple, and repeat it enough times and peeps will begin to believe - there's no smoke without fire.
Then there's confirmation bias. Peeps are more inclined to believe stories about $the_opposition.
Echo Chamber. Peeps only pay attention to anything that supports their view. And will ignore those that challenge their world view.
It's the constant drip, drip, drip: Oh look he/she/their are at "it" again. And there's fatigue, peeps simply get tired banging their heads against a seemingly unbreakable able wall.