I love how you're admittedly making stuff up that the article doesn't say, and then attack it for it.

To be fair, I can somewhat see what causes your misinterpretation. The first sentence about Burning Man is

She said he invited her to Burning Man, an annual festival in the Nevada desert, the following week.

What's cause for confusion here is the interjection defining Burning Man. Your interpretation sees it as a retelling of her experience, i.e. him having to explain her what it is.

But any semi-regular reader of the NYT will take this for what it is: an explanation of Burning Man to the reader.

It's rather common to introduce new terms in article in this way, whenever they are first mentioned. Sometimes, as arguably in this case, it is overdone. Worst offender here is the Economist: "The US, a large north-american country,...".