David, where-ever you got that impression is just plain wrong, or misunderstood.
The purpose of setting the white balance is to give your image the look you want, as the artist. Notice I did not say to make it look "right".
Key here is perception. When a human looks at a room lit by incandescent light, or another by florescent light, we do not consciously think "this is really yellow" or "this is really blue". Our minds adjust automatically.
If you shot the same scenes with a camera without some white balance adjustment, however, the resulting images (which we see out of context -- against a computer screen or similar) will look horribly yellow or blue. They are not so much wrong, as wrong-in-context. Maybe one day when we are all seeing things with virtual reality devices and are immersed inside the original scene, what we will want is a realistic reproduction.
But for images we use online or in print, and see out of that context, what we want is an image that conveys what we (as the photographer) want people to see. And for most of us, we want them at least somewhat corrected. The VERY yellow may remain warm, but we typically want them less yellow. The VERY blue of florescent or mercury vapor we want pulled back warmer, so they may appear bright and "cool" but not as bad as an uncorrected shot.
How much we correct them is a matter of taste. Even for automatic white balance in cameras, the higher end cameras let one specify how to correct, e.g. whether to err on the warm or cool side.
But as to the dropper-- you really do have that backwards. You want something that in real life is neutral (all the same values if you had a light meter at the scene of taking the shot at that time). If in the image it ALREADY shows the same values, the white balance is in theory the same as the scene. If not, you select it, the program forces the white balance so that object then has equal RGB and looks neutral. AFTER your choice it looks neutral, not before (if both before and after there is no change).
But don't think of it as a scientific, numeric thing so much as a matter of taste. It CAN be done numerically, but often the result is not something people like, even if "right". Find a technique that gives the look you want. Starting with a calibrated monitor of course.