It's a Cantonese saying "Anything that walks, swims, crawls, or flies, with its back to heaven is edible.", used in South China. It backdates to the 1800s. It's been referenced in some cookbooks (e.g. "The Chinese Kitchen" by Eileen Yin-Fei Lo), and is known/used by some Chinese, and not others.
Cue supposition based on some searching: the area traded heavily with the West during that time. Take the exotic delicacies and dishes concocted by chefs, add in a language/culture barrier,good old prejudice, and the loss of context in repetition...I can easily imagine it's a Western generalisation/mild slur that got repeated and adopted and over time became adopted as a regional motto of sorts (i.e. isn't 'known' in the Mandarin areas, just the Cantonese south).
Could be waaay off though.