Meaningless anecdata, but as a child and teenager I absolutely loved milk (I was drinking 1 liter of it a day in my teen years). I grew to be 190 cm (around 6 ft 3 inches), whereas both of my parents are around 1 foot shorter.
I loved milk but it didn't counteract Italian genes, I'm 5 foot 6 which is fortunately normal in my country (Uruguay) but would be short-ish in the USA.
