From my experience, veganism is driven by moral imperative, which means facts are secondary to belief. Ergo, there's no strong incentive to control for facts that could influence the interpretation of results.

Now let's take a look at the facts which are reported so we can do our own interpretation. First, total calories on low-carb - 1,000. We can interpret this to mean a tiny amount of fat - it's not low-carb, it's low-fat. Our interpretation is supported by this phrase "...stuck in the low-carb, high protein diet mentality." Next, this phrase "...I was literally starving." We can interpret this to mean "I was hungry all the time." This confirms our interpretation of the calories/fat. The only logical inference is that she was eating a whole lot of carbs anyway, which kept her fasting insulin too high to allow fat to be released from fat tissue, so she omitted that part of her "low-carb" diet from her story. This explains the failure.

To explain the success on that high-carb diet, it's a little tricky. A priori, vegans tend to lie outright about what they actually eat (they eat meat, but they won't tell you - moral imperative, remember?), so it's impossible to determine what she ate just from her own words. But there's one phrase that explains it all "I want to lose about another 15-20lbs, and I know that I can without feeling deprived or miserable." (relating to her new "high-carb" diet) We can now interpret this to mean that she began to eat a whole lot more fat, hence the lack of feeling deprived and miserable. This is supported by her report of total caloric intake - 2,500kcals.

Our above interpretation of her failure and success is supported by experiments such as the Minnesota Semi-Starvation experiment, and the Bellevue All-Meat trial. In the first, constant hunger was common to all subjects. In the second, total lack of hunger was reported. However, in the first experiment, there was weight loss, so using a third experiment - the A-TO-Z experiment - we can now interpret this to mean that the carbs she ate on "low-carb" was mostly refined wheat and sugar, rather than fibrous turnip and cabbage. Ergo, WSLF is actually a low-carb diet in disguise, it omits or reduces refined and easily digestible carbs such as wheat and sugar. I searched that website for some reference to WSLF, and found a list of similar diets pushed as "advocated for milleniums", which is complete poppycock but that's besides the point. In that list, there's the Ornish diet, which is one of the four diets tested in the A-TO-Z experiment, and has been found effective but inferior to the Atkins diet is all measures including weight loss, further supporting our above interpretation of her failure and success.

Finally, the story is an email presented as a testimonial for whatever that website is selling. We should all be familiar with intarweb testimonials by now, so there's basically zero credibility in there. Ya, I know, this sounds like a sweeping dismissal, but that's how it goes with testimonials in my book.