While it doesn't address the "massive emotional payload" bit, Russell's Teapot is the canonical example of an argument that's easy to make and almost impossible to categorically disprove, despite being factually inaccurate. Now imagine that but about a topic people have strong opinions on, and you get something that requires so much preamble to disprove that those who believe it aren't willing to hear the rebuttal.
Basically, you just make something up entirely. If you say that 100,000,000 Americans are killed every year in skiing accidents, that's easy to disprove. But if you post a clip of someone getting punched from an obscure 1970s sitcom that only aired in Hungary and then claim it happened at a restaurant in Denver, that's going to be a lot more difficult to disprove even if the claim is extremely dubious unless you're lucky enough to know the original context.
Some of the more common examples of this in recent times include faked tweet screenshots (mildly difficult to disprove as Twitter's search isn't very useful, and the liar can just say "oh they deleted it"), anecdotes about meeting a celebrity and them doing something unacceptable (basically impossible to disprove unless the meeting DID happen but the incident didn't and eyewitnesses can vouch - see also: the Gritty incident), and videos being used to smear a group despite none of the people involved actually being from that group (reverse video search is extremely difficult, and that relies on it being something previously published rather than recorded explicitly for misinformation campaigns).
Basically, you just make something up entirely. If you say that 100,000,000 Americans are killed every year in skiing accidents, that's easy to disprove. But if you post a clip of someone getting punched from an obscure 1970s sitcom that only aired in Hungary and then claim it happened at a restaurant in Denver, that's going to be a lot more difficult to disprove even if the claim is extremely dubious unless you're lucky enough to know the original context.
Some of the more common examples of this in recent times include faked tweet screenshots (mildly difficult to disprove as Twitter's search isn't very useful, and the liar can just say "oh they deleted it"), anecdotes about meeting a celebrity and them doing something unacceptable (basically impossible to disprove unless the meeting DID happen but the incident didn't and eyewitnesses can vouch - see also: the Gritty incident), and videos being used to smear a group despite none of the people involved actually being from that group (reverse video search is extremely difficult, and that relies on it being something previously published rather than recorded explicitly for misinformation campaigns).