The Kindle is effectively "off" in standby mode. You can't send books to it, unless you use a USB cable, in which case it boots up in USB mass storage mode. Or is wifi still on on the Kindle 3?
Funny, I send books to my Kindle wirelessly all the time in standby mode, and when I wake it, they're already there. Perhaps you're confusing standby (displaying an image, from either the ~4sec power button push or inactivity timeout) with the off setting (~15sec power button push).
