The booting cold without the energy saver set to do that is pretty weird, but out of curiosity have you used any automated backup software in the past? I'm pretty sure I've used backup programs that have an option to tell the Mac to boot itself at a certain time for backup purposes, and that doesn't show up in the Energy Saver (not sure what it's setting).
Definitely there are ones that will auto-wake the Mac using something other than the standard energy saver pref, and I'm pretty sure booting is possible as well.
Perhaps one of these set it at some point in the past and now that you're not using it it's still left the "wake at..." flag turned on?
On a related note, my UPS has a tendency to wake my tower every time there's a slight power fluctuatio that causes it to kick in for a second, but as with most (all?) USB devices that won't boot it, just wake it.