When using Windows, screenshots are captured with your monitor profile embedded, rather than the correct image profile. And you're right, this is definitely a problem.
However, I've never explored third-party screenshot apps. Maybe there's one that captures colours correctly?
Two layers:
First, a Channel Mixer layer at 60% opacity:
Green channel changed from 0/+100/0/0 to 0/0/+100/0
Then a Hue/Saturation layer at 100% opacity:
Reds 0/+25/0
Cyans -10/-60/0
Learn more about this in the Creativity Class.
Well, if you make your layer panel thumbnails bigger (by clicking on the little submenu then choosing "Panel Options") does it help with your confusion?