It's not just that vegetarian diets are "fine" - there's actually a wealth of evidence that a meat-free diet is far healthier - in terms of risk of heart disease, high blood pressure, type-2 diabetes, and various forms of cancer, for example.
Fyi, the creator of that website (Dr. Gregor) can be pretty biased. If you google reviews of his books (from other doctors) you'll see that he sometimes leaves out important details from the studies he cites.
Thhere's also evidence for the contrary. If you care about any dieting at all and watch your micros and macros, you will invariably be above average in health.
Really? There's a body of evidence that a meat-containing diet is protective against heart disease, type-2 diabetes, high blood pressure, and cancer, versus a plant-based diet?
I'd genuinely be very interested for those sources to be shared, please...
That first study compares to meat-containing diets with each other, see the methods section.
edit: I also have some doubts on the care taken in this study and it's peer-review. As there is an easy to spot mistake in table 2 (the dietary fat section).
Studies on human nutrition are extremely limited. If you'd like to see a case reports about keto eating putting Diabetes Type 2 in remission see below:
https://nutritionfacts.org/introduction/