You know, if a CFI wants to help someone (read: 1 person, not anyone) save some money by not charging, that's fine to me. But don't advertise it!!!
When I was getting my private in high school, I didn't have much money and I only worked a part time job so everything I made went towards flying. My instructor was kind enough to not charge me for my flight hours (I still paid for the plane) so that I could afford to fly. He realized that by forgoing a couple hundreds bucks, he was offering the chance for me to achieve my dream. He didn't need the money anyway. I have since payed it forward and have been training a close friend for his private, and no, I'm not charging him. I feel satisfaction in knowing I can provide the same opportunity that was given to me. As far as I'm concerned, doing this for 1 person is not an issue.
Just my .00000012 cents.