Suppose you have an apparatus for mixing paint from two sealed, opaque cannisters and delivering the result into a third clear cannister. The process is simple enough: load the two starting cannisters, one on the left and the other on the right, turn the machine on, and wait for the third cannister to fill up. For the sake of simplicity, we'll assume that the apparatus works as indicated, doesn't get clogged or retain leftover paint from one operation to the next, and that we have an unambiguous and simplified definition for each possible color of paint we could use.
You take a sealed cannister of paint that says "Yellow", and another that says "Blue", and you load them into the machine, and low and behold green paint fills up the third cannister. The question now becomes, what can you say with certainty about the first two cannisters of paint? You can't say that they are labeled correctly (they could be reversed, after all, and you'd still get the same result). Hell, both could be simply filled with green paint. A better test would be to put two cannisters labeled yellow through the machine, and see if you get yellow out of the deal...but even then, you're assuming that every cannister is labeled with equal accuracy or inaccuracy.
The limitation on what you can or can not know is clear: the cannisters you start with are sealed and opaque, so unless you change those conditions somehow you will always be operating under a certain amount of assumption. That's the essential lesson of the Paint Mixer Problem - to comprehend the constraints on your own understanding and to acknowledge them.
It isn't practical (or even feasible) to insist upon 100% transparency, disclosure, and detail from life's paint mixers, relationships, job interviews, or whatever, but it is probably a good idea to be aware of the limitations on your perspective and understanding in any endeavor. It's always nice to know what you're working with, what you can count on, and what is entirely out of your control.
That being said, sometimes all you want is the goddamned green paint, and you don't care if it's made from yellow and blue or from ground puppies and someone else's dreams.
