I’ve heard the same thing.
I suspect, though, that this idea developed as more of a post-hoc rationalization only after the establishment of the ‘small pieces’ cooking style (which was necessitated by limited fuel)
Wikipedia claims that the chopsticks are used because they neither stab nor cut (like knives) and therefore were more civilized and promoted familial harmony at the dinner table. That sounds like retroactive justification to me rather than an explanation why they were invented.
Given that chopsticks date back thousands of years to somewhere near — or prior to — the beginning of the Bronze Age in China, I’m gonna hazard a guess that they were much easier to make than forks and didn’t require widespread availability of metal and metalworking. Bamboo is a plentiful and fast-growing plant there, and to make a whole set of chopsticks you need only one knife, or perhaps a sharp stone, with which to split the bamboo.
Forks sprang up much later. One could guess that metal and metalworking was more common at that time — not just in creating metal tools, but in wandering tinkers to repair and/or replace them. This access to metal may have facilitated the fork’s invention, as a fork made of another material isn’t particularly durable or useful.