> During the job interview, she said he told her that he and his wife were “polyamorous,” a word often used to describe an open marriage. She said he invited her to Burning Man, an annual festival in the Nevada desert, the following week.

Oh, commas and sentence structure, so important.

One says Burning Man was the next week, entirely possible because she thought it was talking about the job (leaving aside -that- naivete), and makes him a liar, in that he couldn't have "believed that she had been informed that she didn't get the job" if he invited her during the interview.

The other says the invitation came the next week.