So, looking at the rules, and I noticed that there are a few good ways to get Unnatural Characteristic.
Infamy is a characteristic. Therefore, it appears to be possible to have a character acquire it.
How much of a Bad Thing is this? I mean, its basically a plus X infamy points, and a X/2 extra DoSs on a acquisiition test/any other infamy test. That seems to be fairly powerful.
More specifically, consider this with Protean Form (p. 220)