I think that statement is true, but not while maintaining or improving standards of living. Increasing population while at least maintaining the standard of living cannot decrease consumption as by any metric standard of living is the very definition of more consumption (more people having running water, heated A/C houses, cars, using the roads, entertainment, better/fresher food, travel, appliances, whatever).
My point isn't in support of Malthusian theory (although Malthus was undeniable correct, its simply matter how far out you care to look) that with one more person we're going to starve to death. Instead its about standard of living. Its an undeniable equation that resources are finite, increases in population increase demand, increased demand with a (at some point) inelastic supply equals higher prices equals less to go around.
The solution is not at all draconian population control. In fact in high consumption nations the populations would control themselves were not for government intervention - immigration, tax incentives for reproducing etc. People in wealthy nations don't have 6 kids (mostly). However for the politicians, pop growth is the most obvious solution to addressing budget shortfalls, overspending (let there be more tax payers) and endears them to business (expanding markets makes it easier to hit growth targets). Meanwhile, the cost to all of us is ignored - increased consumption, high prices/more scarce resources, less functional urban areas etc.
People should realize that quality of life (both standard of living and intangibles like cleaner air, and less traffic etc) will only come from a higher GDP per capita not a higher GDP and that in many ways increasing the number of people degrades the quality of life