The problem with many vehicles with the radiator fluid level sensor is the sensor itself. As you stated, the level and strength appear OK. The sensor is located in the overflow container.
I am having the same problem with my Cadillac CTS as a warning comes up when I first start the car. I can releive the alarm on my control panel and do not see it until the next time I start the car. Unfortunately, many cars with the sensor are not that sophisticated and they trigger an idiot light instead.
With my wife's Tribute increasing the fluid level in the overflow tank solved the problem. The problem was occurring in the winter when the temps caused the fluid to contract more. When the car warmed up the fluid expanded and lamp turned off. The fluid level in the tank was above the low level mark even when cold, but I guess manufacturing tolerances can account for some of the slop.