I like the opinion you should first figure out if the person even wants to learn. I've seen plenty of folks say things like "programming is hard", or "I'd be afraid of screwing something up" because they really aren't interested in it. I think it takes a special kind of personality to find this stuff fun.
If you think you really do have a potential programmer on your hands, then I suggest finding ways of getting into programming topics that reduce risk. Here's a few that were used on me, pretty successfully:
Keep it on paper - you can write pseudocode, encode bytes of ASCII, and play with the concepts of memory allocation without ever getting near a computer. The worst you will risk is a case of boredom.
Work in a reassuring environment - teaching environments are often ways to write code that doesn't get close enough to the core of the computer to really screw things up. Web development, Java development, etc - this stuff can all be taught with abstracting a lot of the harder setup stuff (make build files, set up the web server), so that the student can focus on the act of creation. For me, the act of making code that does something is the light bulb of "aha! I can do this!!! Programing isn't scary!" that I need to get past the fear.
Plan on recovery methods and low risk systems if you are working close enough to the hardware to really do a number on the OS. This is like running OS classes on out of date workstations that no one else uses, or having a spare computer or host device for deploying code - don't do it on the computer that is your one lifeline to the outside world. That way if sometihng goes hideously wrong and you need to rebuild the OS - no big deal.
I don't think fear is totally irrational when you're talking about programming. Computers aren't cheap, and we depend on them for alot. Telling someone that programming is awesome because it means you get to change the fundamental nature of how a computer works is inspiring, but it's also terrifying for someone who knows that they don't know much about the topic.
So accept the fear and figure out ways to approach the topic that mitigate the fear.