First, radical dietary changes cause rapid fluctuations in weight regularly. Not fat, weight.
Second, if you eat only one thing or are generally restrictive... You will probably lose a lot of appetite.
It's no good going off on some theory about pottasium. Occam's razor suggests that this also works for the been soup diet, fruit diet, etc.
It is, potentially, useful to do these kinds of things as an isolation diet (gradually add back foods and pay attention to effects). It's also useful to just break bad habits by doing weird stuff sometimes.
I'm Irish. I love potatoes. They do not have magic dietary powers. The potato doesn't explain anything. You can get similar results with toast, bacon or bananas. The results do not mean anything specific for longer term fat loss, health, etc.
It just proves that bodyweight fluctuates in response to radical diet change. That is known.
Same for a lot of the "water tricks" that thankfully have started to die down. They use bodybuilder tricks to eventually dehydrate themselves for a perfect look on stage day. It's sold as a weight loss trick.