I reject this statement wholeheartedly, and find it a pretty disgusting stance. The idea that the only reason not to kill someone (or otherwise act ethically) is due to religion is horrendous, especially given most religions historical track record on murdering others and other ethical violations.
"Maybe killing people is bad. How do we get people to not do that? Tell them god said not to!"
It starts from the ethical perspective, and uses religion as the blunt hammer to drive it into the masses.
However, that doesn't say much about whether religion was necessary for morality to substantiate. In fact, so many immoral things have been carried out in the name of religion, that you might as well wonder if we would have been much more morally advanced by now if it hadn't been for religion.
Kind of an unanswerable question, but I think my tentative answer is "not really." Mostly because the moral viewpoints that underly atheistic criticisms of (usually Christian) religion tend to themselves be derived from earlier Christian ideas. I don't think it's likely that we'd have a universalist sense of democracy/human life without the underlying Christian soul concept. The Romans, for example, had no qualms about human life being divided into "valuable" and "not valuable" groups.
You could use the criticisms of someone like Nietzsche against Christianity and say we'd be more advanced without it, but I don't think this is probably the type of "advanced" that most people today would have it mind.
That's an extreme claim that requires extreme evidence. You don't just get to pretend your preferred interpretation of a history that humans don't even have (prewriting society) is correct just because you want it to be.
Yes people have done horrible things in the name of religion. But you still can't talk about morality without talking about religion. (And I'm an atheist)