You and I seem to have a lot in common when it comes to this topic. The wife and I like to give on the down low as well. You are right about policy, and then there is all the administrative overhead these organizations can have. Regrettfully there are a lot of scams out there too, so I have become a lot more skeptical of organizations.
I can remember my face burning with shame when my mother would send us to the neighbors to ask for milk or a cup of sugar. She didn't want to do it, so she sent us. I always try to keep the dignity of the person in mind, so that they can accept help without being shamed in front of other people. If they don't know you gave the gift, they don't feel beholden to you, know what I mean? I also believe that good deeds come back to you in one way or another when you need them the most. :)
Yep, I know exactly what you mean.