10.8.3 came through Internet recovery for me when I did a fresh install on my Mac mini 2011 server a few days ago, but at the same time I did my Mac mini 2012 i7 2.6 quad and it loaded up 10.8.2. I then had to update to 10.8.3 via software update. I am guessing the 2012 mm was treated differently because of the fusion drive. It has a special version of disk utility.
With both of those processes I hade a completely wiped drive and did ir via cmd-opt-r.
Your 2011 Mini would have come with Lion, and if it had really been Internet Recovery (IR), it would have installed Lion. I assume you had to enter your AppleID to get Mountain Lion?
The command-option-r boot seems inconsistent from machine to machine. It is supposed to go to IR, but for some machines it seems to detect there is already a working Recovery HD present, so it just boots off of that, which in your case is a Mountain Lion Recovery HD and that reinstalls Mountain Lion.
This issue is mentioned in the
article I linked in my earlier post.
This keeps coming up when people are trying to get back to Lion to sell their Macs. Sometimes IR works to get back to Lion, and for other Macs it just refuses and boots off Recovery HD. The sure way to get back to Lion is to boot from an external USB key or similar and erase the entire drive (not just Macintosh HD), so the Mountain Lion Recovery HD is gone. Then it works like it should.