Thank you, Ms. Gause,
I think you are on to something here. I experimented with it some, using not just red but other colors, like blue, yellow, etc., finding that I had some interesting results.

This is the first time I had chosen a color for the path. I then clicked "OK."

I clicked on the Color Picker fill box the second time. Notice that the slider is now at the top, red-purple end of the spectrum. 
Going to the Color Picker for the third and last time, I then noticed that the circle had moved automatically to a state, that was not causing any exclamation point to be indicated.
This seemed to be the same trend when working with other colors. As far as I can tell while using a NEC Color Critical monitor, the path did not change color at any point of time. Does that mean that it had been at the same place one the color spectrum slider all along, but just not indicating it?
Sand Patch
When working in CMYK, your color automatically gets converted to something that can be reproduced with the color profile you're using.
When working in CMYK color mode, it doesn't make a lot of sense to use the color picker at all. Use either the color panel or the swatches panel.