The statement is generally an accurate one concerning avoiding turbulence on flight routes from the pacific region of the US to Western South America (Chile/Peru) as the flight route stays largely away from any mountains or large areas of land and most importantly avoids the rain forests of Brazil which ALWAYS have a large amount of ITCZ activity. You can also avoid this area flying into Chile from the US, as most routes tend to cross over to the Pacific in Central America and skirt the coast all the way down instead of flying right over northern Brazil.

You wont be able to avoid this area flying to EZE from the US however, Ive probably done EZE 15-20 times and its almost ALWAYS rough at one point due to the weather over the rainforest.

The statements saying its always rough crossing the ITCZ is not true-its not always. Ive had plenty of smooth crossings to Australia/NZ (I do this 4 times a year and have for 15 years). It just depends on where the weather systems line up along the TPAC route plan. The only route I can say Ive always had some turbulence is crossing Brazil. (Ironically 10 days ago coming down to NZ on a 787 was the roughest prolonged turbulence ive ever had-it was 7 hours nonestop.