By "programming" here I just meant someone who writes (or modifies) even a small amount of code. We found that this was always an extremely small fraction of users, even in the easiest cases.

I certainly agree that self-identifying as programmers would be totally the wrong criterion.

Consider the number of people today who edit a URL in their browser location bar (for example to delete unnecessary trailing information if they are going to email it, or to try to fix it if it doesn't work). I bet a good study of a representative user population would find that only 10% or less would do this even if it was suggested.

If someone is willing to do that I'm willing to consider them a programmer in this context. They have made the basic leap to understand how to map between text and behavior, how to debug, etc.