I think mine is called the early 2009 Mini, a similar generation, and I'm running latest and greatest Mavericks:
Model Name: Mac mini
Model Identifier: Macmini3,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.26 GHz
Number of Processors: 1
Total Number of Cores: 2
L2 Cache: 3 MB
Memory: 4 GB
The first thing that came to my mind was that I also might have seen that message but proceeded anyway because I could. Today blocks are set up to warn consumers off because they'll think features like ThunderBolt and LIghtfoot are available on their machines just because they saw it on TV. I'd be disappointed too if it turns out I could upgrade everything I needed but there was some system gestalt thingy that wouldn't let the installer proceed.
So what was a black MacBook Pro originally? Wiki says they started as Core Duo and moved up to Core 2 Duo and 8GB RAM OEM, only addressing 4GB, so I imagine there's trouble with Mavericks trying more addresses on machines that don't have them available?
I would expect to move from Snow Leopard, to Lion (to Mountain Lion), and to Mavericks out of hand, because they shipped that way new before the air style took over. Do you have 160GB boot drive, at least room enough to copy the whole thing down? Also, something in the middle was a paid upgrade, so is the Mavericks blocked by the fact nobody is allowed to jump that far ahead past a paid jump?