Is this JWST flash report enough to tell what happened?

The first thing I’d look for is the underlying observation or a paper from the researchers involved. The report as described doesn’t give a sky position, instrument, observing filter, images, or a technical analysis, so there isn’t enough here to check the claim independently.

Also, two detections 88 days apart don’t by themselves show that one object produced both flashes. The observations would need to be compared carefully, including whether the apparent position and signal match.

“No known object at that location” can mean several things. It might mean no catalogued source was visible in the images, not that the region was literally empty or that every ordinary explanation has been ruled out.

Researchers would generally check the data for processing or detector issues, compare the signal across images and filters, and consider whether a transient or moving source could explain it. Those are possibilities to investigate, not explanations established by this report.

I’d hold off on the “astronomers are stumped” framing until there’s more than a dramatic summary. Useful evidence would include the original observing records, an analysis showing the signal in the data, and an explanation of what checks were done. Without those details, the honest answer is that the claim is too thin to judge.