Aha! I think I found the problem, and it's NOT with Cell Statistics.
As I mentioned, most of the out-of range data were in Florida. The data are projected minimum January temperatures, and of course, in the US, South Florida is among the hottest places in January. The Cell Statistics Data are correct, but the statistics in the Symbology classifier are wrong. See the image below. I selected an especially hot year (2072); the classifier says that the maximum value is 284.7843018 (ok, these temperature data are Kelvin BTW, not Celsius. Otherwise we would be in deep doo-doo). So I classified into two groups, with 284 as the cutoff. The classifier says there are 6 elements above my cut-off value. But, if you look at the partial image of Florida, You will see a lot of 6 cells colored red. And if you look at the "identify" box, you will see that the pixel I have identified has a value of 285.128021, well outside the range that the classifier says exists in the raster. I clicked around in the red area, and there are more than 6 unique values. Stack up 30 rasters (years) and South Florida will show lots of these "out of range" values. So, I am convinced that the Cell Statistics values are correct, and there is something wrong with the Symbology classifier. Which does not bother me right this moment.
If anyone can shed light on this problem, I'd be happy to hear your input.