Consider my assertion: "The Wikipedia featured article today is on Uriel Sebree". Even if you haven't checked Wikipedia today and have no evidence on this topic, you're likely to believe me. Why would I be lying?
This can be nicely modeled in Bayesian terms - you start with a prior evenly distributed across Wikipedia topics, the probability of me saying this conditional on it being false is pretty low, and the probability of me saying it conditional on it being true is pretty high. So noting that I said it nicely concentrates probability mass in the worlds where it's true. You're totally justified in believing it. The key here is that you have no reason to believe there's a large group of people who go around talking about Uriel Sebree being on Wikipedia regardless of whether or not he really is.
Unsupported assertions about controversial topics
The example given in Morendil's post is that some races are biologically less intelligent than others. Let's say you have no knowledge of this whatsoever. You're so naive you don't even realize it might be controversial. In this case, someone who asserts "some races are biologically less intelligent than others" is no less believable than someone who asserts "some races have slightly different frequencies of pancreatic cancer than others." You'd accept the second as the sort of boring but reliable biological fact that no one is particularly prone to lie about, and you'd do the same with the first.
Now let's say you're familiar with controversies in sociology and genetics, you already know that some people believe some races are biologically more intelligent, and other people don't. Let's say you gauge the people around you and find that about 25% of people agree with the statement and 75% disagree.
This survey could be useful. You have to ask yourself - is this statement about race and genetics more likely to have the support of a majority of people in a world where it's true than in a world where it's false? "No" is a perfectly valid answer here - you might think people are so interested in signalling that they're not racist that they'll completely suspend their rational faculties. But "yes" is also a valid answer here if you think that the people around you have reasonably intelligent opinions on the issue.