Resolved

The Trib follows up on my mystery:

Allred described her client as a "registered Republican," though Bialek does not have an active voter card in Illinois, election officials said. The state does not allow voters to register by party, but records show she pulled a GOP ballot in the 2008 primary.

So she's not registered to vote at all right now, but she has voted in a Republican primary at least once. That doesn't have quite the same ring as "registered Republican".

I like the way the Trib doesn't actually come out and say that Allred was befuddled.
But at least ONE part of the story is no longer muddled.