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That is partly true, and partly false:

Vitamin D plays a role, but not the sole role; the same is true with genetics.

Vitamin D is NOT a vitamin*: That is the official/legal name that the FDA recognizes. It is made in response to insolation (incoming solar radiation) upon the epidermis by converting 7-dehydrocholesterol into the active steroidal hormone.

Diet plays a major role in how much of that precursor the body produces. Sunlight plays a major role in how much of that precursor is converted.

Other major factors are that few people in “civilized” nations expose enough skin to full-spectrum sunlight - especially in the cold months. The darker the skin, the more that sunlight is needed. Indoor lighting is dim and, with few exception, is not adequately full spectrum.

* Vitamin:

The proper, consistent, scientific definition of a vitamin is: an organic compound that the body MUST have to be healthy, i.e., to prevent a deficiency state (disease), but that the body CANNOT make.

Cholecalciferol (Vitamin D3) is NOT a true vitamin - it is a steroidal hormone - but the government has decreed it to be one. One need not ever ingest actual Cholecalciferol to have an adequate supply of D3; one need only eat proper foods and get adequate sunlight on skin. The associated deficiency state - Rickets - is not alone sufficient to make it an authentic vitamin.

Linoleic Acid [18:2 Omega-6] and Alpha-Linolenic Acid [18:3 Omega-3] ARE true vitamins, but the government has decreed them not to be ones. That is why nutritionists, in retaliation, named them Essential Fatty Acids [EFAs]. The body cannot make either one (although it can make derivatives from them via Delta-6-Desaturase, e.g., Gamma-Linolenic [18:3 Omega-6] and Stearidonic Acid [18:4 Omega-3], and there are consistent known deficiency-state symptoms associated with their chronic lack in the diet.

(See Johanna Budwig and Udo Erasmus, among others.)

If all growth factors [race, hormones, disease, age, country, latitude, altitude, area [city or farm or suburb or mountains], diet, sleep, exercise, smoking, drugs, air pollution, area drinking water makeup, exposure to lead, etc.,] are not accounted for then it is a flawed study.
Impossible to reach such a protein growth determiner as too many variables present. Even a third grader can figure this one out. Did they do a comparative height/protein study on the Dinka tribe? Probably not. As I say, appears to be a totally flawed study.