Maybe it's shutting down for some reason then restarting? If Energy saver is set to Restart after a power failure it would come back up. Maybe the mains loses power, or the power supply or some component in the machine is shutting it off, then it Restarts per Energy Saver settings.

Reset the SMC? -

Shut down the computer.
Unplug the computer's power cord.
Wait fifteen seconds.
Attach the computer's power cord.
Wait five seconds, then press the power button to turn on the computer.

If they set it to never sleep does it do it?

I'm hoping to get a look at her console over the next couple of days
Never heard it put that way. I'll have to remember that one. Geek pickup lines. grin