I am an avid martial arts practitioner, and in our school we have a similar policy to your '3 visits then you need to join the club' rule. Sometimes some one will walk in off the street and we will notify them up front about our policy then invite them onto the mat. Since there is a substantial investment in equipment up front (not like this hobby, thats for sure...) and we don't want some one to go through all that and decided this isn't for them. Some of them come in and stay for a while some don't return after the second class. No skin off my nose if they don't show up again, but when they do it is pretty rewarding. I was really surprised one time to have a guy walk in and say a buddy of his told him about our place, his buddy didn't care for the style but recommended us still because he thought we were quite personable. Now this is inherently a learning environment in which teaching/learning is the norm unlike the flight field. My suggestion would be if you don't want to deal with people walking out on you or not joining the club/AMA or the politics involved then don't offer to teach. Save yourself the headache. Make something up, tell them you're not qualified or don't feel comfortable training, they'll never be the wiser.

BTW, we never had a problem with any one joining after 3 lessons, they either did or didn't.

Lead