Shift+click doesn't work in CS6 (at least ont in 16.0.3). It just selects desired color but not applied it. I didn't find apply color function - i tried to click with different key combinations, click on color boxes, or on numeric value to go to edit mode and acknowledge value with enter key - nothing worked. Illustrator stays blind and deaf for user tries.
What works (beside changing eyedropper inner options):
1) shift+X to swap colors two times, doesn't work if two or more objects have different stroke or fill color (the one we are not interested to change).
2) copy color value from box, enter 0, enter again to the box, and paste copied value.
Many functions Illustrator has seems totally underdeveloped or badly thought and behaves much better in Inkscape or any other alternative editors. Real shame for such big player as Adobe.