False. When you reduce poverty in a third world population, they simply breed more. This has repeatedly been observed. If you want to loosely throw around words such as "fact" and "best", then I submit that the following, although potentially unpleasant to you, is closer to the correct usage: "In fact the best way to lower humanity's impact on the environment is to eliminate third world population."
Gapminder link: www.bit.ly/AiTWsG
Increase income per person in the third world as much as you want, but there will be no permanent, negative effect on population growth for as long as the population is mostly unwhite because income has nothing to do with character, culture, IQ, and all of the other factors at play.