Color Picker offers few options in the Options bar. After activating tool look for Sample Size in the Options bar and change it to Point Sample if you want to pick color only where clicked without to average color from surrounding pixels what is comon practice for files with huge amount of pixels, some people like to say with high resolution.
There is another drop down Sample which also may need attention to pick color that you see on screen. Check what is selected because there are options with no Adjustments what will discard adjustments layers and their effect on pixels on image.
The Adobe rep in chat said "It will never be 100% accurate."
I disagree with support rep. For testing purposes, leave the Sample Size on "Point Sample" as in Bojan's screenshot, then zoom way in until you can see the pixels quite clearly. When you click on one pixel, that is the color the Eyedropper picks up. Then try some of the other options as well. When you are zoomed in, you'll be able to see how the color is getting picked up.