Not sure if this a related but there was another member that had something similar with a new imac and the 3TB non fusion drive. For some unknown reason, to me at least, apple has set the 3TB standard drive model imac to a logical storage group. Which in my opinion it shouldn't be as it is one drive. The logical storage group is for combining 2 drives so they look like one bigger drive. With the 3TB single drive imac that shouldn't be needed.
About the only option you have it to boot to the internet recovery system, hold down the command+option+r keys at startup until you see a globe on the screen, and use disk utility to repartition the drive as one partition and then reinstall the os, all your programs and your files.
In my opinion apple should not be setting these system up like this. That is unless there is something wrong with mountain lion that it can't be installed on such a large single volume without it being set as a logical storage group.
You might have to pack the system up and take it to a apple store and have them fix this mess.
If you do this yourself or you take it to apple for them to figure out and fix it you must make a backup copy of all your data on a external drive as the only way to fix this mess is to wipe the drive, which is what repartitioning will do, and reinstall everything fresh and clean.
In case anyone else has this problem and wonders what happened, it's not great news. I took LowLuster's advice and I spoke to Apple and they resolved the problem for me (it took quite a few hours). Unfortunately the steps taken were too long for me to remember, so if anyone else has the same problem the best thing that you can do is speak to Apple.