Genetic topics are eventually meaningless cuz we cannot change anything about our genes, and relevant surgeries will be very expensive and perhaps very dangerous to turn you into freaks.
I don't know if that's true,cuz I can't find any scientific papers that can back up theories that meats, eggs, dairies are impacting on heights more than any other nutritions.
I think if you can guarantee not to starve and be malnutritional and still can't get rid of short, then either will the reason be your genes or random hormonal diseases like dwarfisms, Turner's syndrome and similar diseases.
But I assured this theory through digging into the Netherlands', Germany's, and Sweden's cuisines, indeed they are highly enjoying meats, breads(I think they tend to involve eggs into them) , dairies, and these three countries are the top 3 tallest countries throughout the world. (the Netherland's productions of dairy are astonishingly handsome while German's productions of meats are sharing 99% ratio of the whole Europe's meat assumptions and Sweden is also highly prone to meats and diaries)
BTW:Actually the top 3 tallest countries are not these three. The true answer is South Sudan, Montenegro, and Bosnia(where Meck was grieving his height so that he made his mind to do LL for even 18cm growth LOL), but I have no clues about their exact nutritional and ethnic situations so I cannot be too bold to judge if the conclusions are right or not through these countries.