On the other hand, Daniel Kahn points out in his book on thinking that if you ask someone to work out a multiplication sum (complex enough to need working out) in their head while they are walking, they are likely to stop in order to do it. It seems that the two activities compete for the same mental resources.
With this in mind I'd tentatively suggest that the way in which walking boosts creativity isn't so much by adding some new element that wasn't there before, as by helping to block out interference from distracting mental processes that would otherwise get in the way. States of creativity (like safe driving) often seem to involve a degree of withdrawal or shutting out, as well as of opening up, and I suspect walking helps achieve that.
By the way, having rejected mindfulness as a solution to motorway panics (as per my recent post), I'm now trying sugar free gum for the same purpose, and with much greater success, having heard that the act of chewing tends to suppress fear. I suspect it performs much the same "shutting down by interference" function as walking, in fact. Just don't try to do both at the same time.