I remember a few years ago participating in a massive thread on the BBC website about lunar and other planting. Despite numerous invitations, none of the supporters of this method could come up with any supporting evidence. As several posters have said above, you need to sow when you get a chance and when the weather and soil are suitable.
Unless an independent person or institution gets around to doing genuine, monitored, comparative trials - and someone might be able to point me towards some - I can only conclude that it's a lot of woffle.
I suspect that people who claim to get good results owe any success to the fact that, being slightly fanatical about it, they take particular care to get all the other variables right and so give the seeds/plants the best chance.