No third party software, your screen shot is what my system looks like. I'm pretty sure the options have changed from Lion though. In Lion the description was slightly different which was "put computer to sleep" where it actually entered sleep mode instead of just turning the monitor off.I never put my mini to sleep, so I haven't noticed any sleep problems.
Are you using third party software to put your mac to sleep using a hot corner?
Under Mountain Lion, the only hot corner option I saw related to sleep was display sleep (see attached).
I have a mac mini late 2009, with 120 GB SSD and 8GB ram. It runs really fast but since I installed Mountain Lion, but at least once a day finder keeps crashing. I'm really frustrated by this, as I can't backup my docs because the backups take longer than time between crashes.
The upgrade process killed my HD, hence the shiny new SSD. Would recommend full backup before upgrading!
Originally sophos antivirus was crashing the machine, but upgraded to latest and that stopped (or maybe it hasn't?- perhaps I should remove Sophos AV altogether?)
Anyone else with similar experience?