That is conventional wisdom, but it is not scientifically accurate. The low IQ in the mohammedan world is in part a product of inbreeding depression; other parts of the difference are harder to account for but the difference is real, and heritable. It does not result from environmental factors, nor can it be cured by them.
Saudis and other wealthy Gulf Arabs, for instance, are not the least deprived, but they're still statistically speaking one standard deviation behind Europeans, who are themselves 0.8-1.1 or so SDs behind Ashkenazy Jews.
d.o.l.
Criminal Number 18F
Inbreeding and genetics are factors too, but IQ is most definitely affected by nutritional factors in utero and in early childhood, especially before age 2. No matter how well you feed them after that, the cognitive damage from malnutrition cannot be fully corrected. The brain is still doing critical growth and development at that age, and the developmental window then closes.