I think it depends on the dog. Mine circles several times until she has found the perfect spot. Some fosters we had would just throw down wherever. I’ll definitely watch the direction next time.
The reason I've read is that it's a leftover from when they lived in the wild, and it would help make sure they don't lay down on top of something dangerous, like a snake or ant colony. It would also make since to do it before pooping since they're going to be in a vulnerable position.
The dataset seems to be robust. Would be even more interesting if reproduced, but I'd be surprised if someone faked nearly 7500 datapoints for the sake of giving dogs a magnetic sense.
There have been no follow up studies that I can find to replicate this “experiment”.
Searching around just finds lots of duplicate stories in the old echo chamber based on the original paper.