They may be right. Their long-term goal is not simply a space program, but a lunar colony; a concept the U.S. abandoned in the 1970s because of short-sightedness.
The Chinese think longer than we do. Imagine, knowing what you know now, that it is the 1800s, and as a colonial power you have the military and technical ability to claim all of the lands that are now Saudi Arabia, and that those lands are currently uninhabited, so all you would have to do is simply go claim them. Would you do it?
The moon has a resource far more valuable than the oil of Saudi Arabia. That resource is Helium-3, which isn't available in significant quantity on Earth. With it (and ordinary deuterium easily extracted from seawater) fusion becomes almost trivial. We have an essentially clean and practically limitless source of energy within our grasps, and we're going to give it away to the Chinese because we are too busy spending our childrens' seed corn on social programs.
Uh...no. D-T fusion is actually easier to achieve, D-H3 makes for a simpler reactor. We are nowhere near achieving the breakeven point for either.