When I search Google for [fish rots from head], the top 3 results each mention some Chinese connection – one calls it a "Chinese proverb", others say it's been variously attributed to many traditions, often Turkish, Greek, or Chinese.

(So: maybe that's an origin. Or perhaps there's something vaguely similar in some Chinese traditions. Or perhaps it's just a common mal-attribution, as there's a tendency in the west to ascribe various highly-figurative or riddle-like pearls of wisdom to "the Chinese", or "the Arabs", or "the Buddhists", etc.)