IMHO when a kid shows interest in wanting to take up music RUN WITH IT!!! This will help shape their minds and thought processes in ways that other pursuits won't which IMHO is invaluable so it really doesn't matter if the child continues to play for the next 50 years or not. It will also give them HOURS of stuff to do to keep them out of places/pursuits that might get them into trouble.
I wouldn't invest in buying an instrument though until the child has enough time under his belt that they are serious enough to contribute to the cost of the intrument. I would look into renting. I don't know anything about guitars, but I know that schools will rent violins, woodwinds, etc...
Smurfy may be a cool mom (which is always good) but she most certainly is a SMART mom (which is even better).