Fill tool problem [SOLUTION?]
I noticed in one of my unrelated projects that the fill tool seemed to be working perfectly well for me - i.e. a single click would give me a perfect representation of the colour I had selected, unlike what you (and indeed I) had experienced with this project.
This gave me a chance to compare a working instance of a Blender project alongside a 'faulty' project to try to get to the bottom of the issue.
I think I have a solution:
If you are using the fill tool in texture paint mode and experience the I-have-to-click-a-billion-times-to-get-the-right-colour issue, in the 3D View toolbar menu, go to 'BRUSH' and make sure that 'Unified Strength' is UNticked (I suspect that it will be ticked if you're experiencing the problem).
Note that unticking this seems to reset your brush strength to 50%, so whack it back up to 100, and try it out. From what I can see, this should solve the fill issue ...
Hope that helps.