I think that is a questionable assertion. Ape swing from trees better than we do, but we seem to surpass them in most other measurements. And humans and apes live side-by-side in many parts of the world, so they share an environment. How then, are apes as highly evolved for their environment as we are?
Basically, we have a postulated common ancester, plus (they say) millions of years of evolution -- and we hit the jackpot with Homo Sapiens Sapiens and they got stuck with Capuchin Monkeys. I don't see it.
That's a bit of a cop-out. True, we didn't evolve directly from any of the modern ape species. However, we're most closely related to the chimpanzees, with whom we share a fairly recent common ancestor. The evidence suggests that that last common ancestor probably looked a lot more like a chimp than it did like us.
"A" in the upper left above is a modern chimp skull. "B" next to it is an Australopithecus africanus from 2.6 million years ago. In fact, "B" up to "N" (a modern human) are fossil hominids of decreasing age. But "A," the chimp, which is as modern as "N," the human, seems to fit in well right at the beginning of the sequence. Again, that last common ancestor looked a lot like a chimp.
What about the grosser mischaracterization that "We came from monkeys?" An ape is not a monkey, but apes arose from monkeys maybe 30 million years ago. If you could take a time-machine voyage to 35 million years ago, the most human-looking species you could find would be some sort of monkey.
In fact, go back far enough, and the "most advanced vertebrate" is some kind of fish. Farther back, and there are no true vertebrates, only chordates. And so forth.