From what I have read, the vast majority of "engine coolant low" messages (despite normal coolant levels) stem from issues with the tank, often a faulty sensor which requires a new tank. I had the same warning light but it was caused by electrical corrosion further up the line, It seems the connector was exposed to water at some point. The mechanic cut off the wires and soldered each wire into a new connector. Problem solved. Total cost including diagnosis was $300 (two hours labor plus 30 for parts).

 

WOW, thank you for update.