Except that's not how it works. An excess of fat can directly cause problems.
Above a certain point, having too much fat causes chronic hypoxia in fatty tissue, leading to chronic inflammation, which can eventually lead to systemic problems like insulin resistance, cardiovascular disease, kidney failure, liver disease, and cancer.
Edit: I am specifically referring to abdominal fat in excess of what a given body is able to cope with.
They merely suggested that weight loss does not occur as a result of a healthy diet, but rather as a result of an intentionally deficient diet (technically an "unhealthy" diet). That you can lose weight eating only potatoes is therefore not very interesting and does not imply that the diet is healthy.
Aren’t all diets whose goal is weight loss “intentionally deficient” ?
I don't have an opinion either way and I don't think this is a likely reason, but it is a possibility.
Anyway the diet described in the article doesn't make any assumption about calories. If you're taking enough calories to maintain your weight but losing weight, then it's very likely there's something else you're not getting enough of.
Besides the fact the diet isn't asking suggesting anyone not supplement, a vegan diet won't lead to a severe B-12 deficiency in a matter months. But hey there is a non-0% chance you are bang on and the people losing weight when trying to eat 20 potatoes a day to meet their caloric demands are actually just noticing the weight loss once they also get pellagra and anemia, they just figured it was a coincidence.
They found that indigestible oils like Olestra served to flush out the chemicals that bonded with oils, so maybe the high fiber potato diet is good for flushing out something else?
From the perspective I took where a healthy diet is a sustainable one with sufficient nutrients and long lifetime expectancy, a weight loss diet is unhealthy and unsustainable, but there to negate a different issue and improve long-term health.
However, a diet that varies in how 'fed' you are over time is very likely healthier than one where you are constantly taking in nutrients. During that post-prandial state, insulin and growth factors are elevated, and autophagy and other important pathways for 'tidying up' sick cells are turned off. That is why I don't think it is fair to say that fasts or restrictive diets are inherently unhealthy, I reckon 'whether this can be sustained steadily forever' should not be the bar. Similarly, the 200% of normal diet consumed after marathon is healthy that day and probably more healthy than eating normally since it is going to allow for repair and replenishment of depleted substrates, but would not be healthy if eaten every day.
For someone with health issues stemming from obesity, a potato-crash diet could immediately improve health, and continue to for a good while.
Adopting a diet that balances nutrients and calories and also provides all needed vitamins will lead to weight loss and health improvement (in most cases).