I think he's actually giving away the image of one of his works every day; the question of whether value lies in the image or in the precious object is interesting but vexed.
There are lots of ways this could work. One obvious example is trading art. Go to the Musée Rodin: he had a Renoir on his walls, he had a van Gogh. Did he buy these at the department store? Weblogs make a sensible entry point to amicable exchanges between artists with similar sensibilities -- even artists who can't conveniently meet every Tuesday at the cafe down the street.
Parker's gifts are restricted by the Creative Commons noncommercial clause. The popularity of this restriction puzzles me. Perhaps the precise meaning of noncommercial is clear to Lessig, but I've talked to dozens of academics and businesspeople over the years about this language and nobody was very confident they understood precisely what it means. I understand the chagrin that people might feel if they gave away an image that later ended up making millions for someone else, but what's the harm? If you use Tinderbox to make a billion dollars, I'd like you to say 'thanks', but either way: how nice for you!