It's plain, 1000 times proven, bullshi*. Don't get another problem to add to any possible height neurosis.
Nevertheless, height neurosis and its ramifications such as depression, yes, can harm cognitive function. And in turn, sadly, some antidepressants and most tranquilizers harm memory capacity. It's another reason in my opinion for a LL candidate to find good continuous support from a good psychologist, or counselling, or coaching, as obligatory part of the whole process, from the beginning, planning phase, until post recovery or until he/she feels necessary or positive.
I did some researches about it recently and I think Wikipedia 'Height and Intelligence' gave the best answer to this question.
And yeah, as the recapulation of the wiki, the statements like 'short ppl are more stupid' is totally bs, not to mention we can find the opposite instances irl like Japanese, which is composed of a lot of intelligent people, including the son of Soft Bank.
Speaking of Japaneses, I read some materials written in the last century, and it seems to me during WWI and WWII, Japaneses were feeling inferior about their race to White and a writer back then described Japanese as 'more stupid, incapable, shorter than White..'(in regard of height it was true).