Regarding the 2013 study on British/working-class New York accents: Actually I believe your description exactly matches the one in the article, which says, participants had "higher false memory rate for the speaker with a working class accent," suggesting they thought that voice was making a mistake, whereas with the British voice they thought it wasn't a mistake and that "the Brit must have said what he meant."
In general, there are two effects at work. One is stereotypes: cultural bias, which led the student in Rubin and Babel's studies to just assume that they won't understand the accent of a Chinese looking professor. Another cultural effect is that high-prestige accents like the British one in Lev-Ari study, are held more reliable.
The second effect is cognitive: we have a tendency to avoid actually listening and paying attention to difficult stimuli, in this case, foreign accents.
These effects are not mutually exclusive. And they also overlap. Stereotypes are partly born out of lazy brains. But they also shape how our brains interprets the world.