Being a laptop, it may have a problem with the lid sensor (in the trackpad actually) being glitchy and thinking the lid got closed. I've seen it happen. You could UNPLUG the trackpad outright (and use external keyboard/mouse) as a troubleshooting step.
That's an interesting thought. I used InsomniaX to disable lid sleep and the same thing still happens, so I think that most likely rules out the lid sensor?
Another troubleshooting step is "separate hardware from software" by booting the computer off an external hard drive and see if the problem persists or goes away. You can also do the opposite by booting the computer in target mode and booting a different computer off it's startup drive. The latter option has the advantage that you can continue to use it somewhat normally while testing.
I haven't tried booting a different computer from this machine's hard drive. I have tried booting the problematic computer from an external drive. Still hibernates.
Finally, peripherals can cause this. Think anything connected over USB/firewire/displayport/thunderbolt/etc. This includes keyboards and mice
Literally the only things connected to this computer are the power cable and an Ethernet cable. Disconnecting the Ethernet and using WiFi didn't help.
I'm leaning more and more to hardware.