The weight loss bits are just silly. Any sustained caloric deficit will cause one to lose fat, regardless of the source. This just seems to be rediscovering the already well-known fact that complex carbohydrates (which potatoes provide) keep you better satiated than simple carbohydrates, so the subjects were consuming less calories overall.
Most people fall off diets in the longer term, and there are various causes, including hunger, but also including things like wanting to be able to partake in social events that feature other foods.
Quite why they have chosen to abandon their diet-scepticism in favour of anecdotes from a guy who literally promoted potatos as his day job and a guy who sells courses on how to eat potatos for $199+, but I guess contrarians gotta be contrary...
But things are not that simple. There is no evidence that simply removing processed food is an effective enough diet to produce the sustained 10-20% weight loss (or more) that many obese Americans would need to experience in order to weigh the same as their grandparents. And in fact there is overwhelming evidence that this modest intervention (and several more extreme calorie restricted versions) tend not to produce durable weight loss in anywhere near that amount.
PS Don’t take this the wrong way. I really really wish that that diet did work. I would pay you literally thousands of dollars to make it work. Because our grandparents ate a very filling and diverse diet, and that diet would be effortless to follow.