This paper is a meta-analysis of studies looking solely at iron stores among vegetarians vs omnivores. It doesn’t broadly address the claim about nutritional deficiencies among those who consume a meat-free diet more broadly. Moreover, among the studies they examined there was significant variability among cutoffs for serum ferritin as indicative of storage iron. About all I can conclude is that premenopausal vegetarian women should supplement with iron.

As do most meat eaters. What's your point?

Exactly. This is evidence that it is hard. I'm glad the person you are replying to is able to manage a vegetarian diet successfully. It's definitely possible to get adequate nutrition, but most people don't have the understanding or discipline required.

Vegan avoids all animal products while vegetarians will eat milk products and sometimes fish. Since the vegan and vegetarian are often used interchangeably, I believe the article is really referring to the vegan lifestyle.