I have heard this sentence for years, but nobody has been able to provide an example whose price was not outrageous. I suppose that this sentence is written by people who do not care whether they pay $5 or $50 for their daily food. Such people are not average people.
While it is possible to compose a vegan diet with enough proteins at a reasonable cost, and I do this every day, it is really hard to avoid gaining weight, much, much harder than with a non-vegan diet, where you have access to cheap pure proteins, like chicken breast or turkey breast.
Ever since I have switched to a vegan diet, a couple of years ago, I have to monitor my weight permanently and I have to take corrective actions frequently, despite the fact that I eat much less than most people are used to.