There is one of her. The reason a claim like this can start to feel plausible on the third encounter is one of the most robust findings in the psychology of belief, and it has a name.
In 1977, Hasher, Goldstein and Toppino ran an experiment in which participants rated the truth of a set of statements across three sessions spread over weeks. Some statements repeated between sessions; some did not. Repeated statements were rated as more probably true, regardless of whether they were actually true. The effect has been replicated many times since and is known as the illusory truth effect.
The mechanism generally offered is processing fluency. A statement encountered before is easier to process the second time, and the brain reads that ease as familiarity, and familiarity as a weak signal of truth. This is not stupidity; it is an efficient heuristic. Things you have heard before genuinely are more likely to be true in an environment where most of what you hear is true. It fails in an environment engineered to repeat things regardless.
Knowing the right answer does not reliably protect you. Participants rated repeated falsehoods as truer even when they could state the correct fact on request.
The uncomfortable part is that knowledge is not much protection. Work by Fazio and colleagues, published in the Journal of Experimental Psychology: General in 2015, tested whether prior knowledge shields people from the effect. It did not, reliably. Participants rated repeated falsehoods as truer even in cases where they could produce the correct answer when asked directly. Knowing a fact and feeling that a statement is true turn out to be somewhat separable operations.
This has direct consequences for how a correction should be written, and most corrections get it wrong.
A correction that leads with the false claim in large type gives the falsehood another repetition, in the most memorable position on the page, attached to your credibility. Over time, the source detail fades faster than the claim itself. What remains is a familiar sentence and a vague sense of having encountered it somewhere reputable.
The better shape is to lead with the true statement, state it plainly, and repeat it. Mention the false version once, clearly marked, subordinate to the correction rather than above it. Give people a replacement account rather than a deletion — a gap in an explanation tends to get refilled with the thing that was there before, whereas a better explanation can displace it.
That is a large part of why this site is built the way it is. The lie is enormous and the correction is set in the same typeface at the same volume, because a correction whispered in grey nine-point type is losing the repetition contest before it starts. It is also why the impossible headline is a design requirement rather than a joke: a claim that cannot survive contact with reality gets no benefit from being repeated, because there is no plausible version of it to become familiar with.
The practical version, for a reader, is smaller and more annoying. When something feels true, ask where you first encountered it. If the answer is that you cannot remember, that is not evidence for the claim. It is evidence that you have seen it more than once.