Not true, at least not in a useful sense (that is, without semantic games like "Putting users first is really putting profits first because it makes them money"). Google often turns down options that would squeeze out a little more money at the expense of its users. For example, Google slapped content farms for being worthless even though they seem to be pretty good money-makers.
But, while trying to avoid the semantics arguement, their profits depend on their advertising, which depends on search qualtity. By keeping search qualtity high they are passing over small, short-term profits for long-term ones. Yes the main idea is keeping users happy somthey stick around, but they aren't doing it because they love their users theyre doing it to make a better business.