Legal consistency

Some time ago I asserted that American court opinions "are fairly accessible once one learns a few key words and turns of phrase". Suddenly I begin to doubt that.

In EEOC v. Lee's Log Cabin (7th. Cir, 2008-10-06) I read this marvellous piece of logic:

The dissent also asserts that "[i]t is undisputed that at all relevant times, Stewart was not only HIV positive . . . but she also had AIDS. So the allegation in the complaint that Stewart was 'HIV positive' is consistent with the fact that she has AIDS." Dissent, at p. 18. No, it's not, but the opposite is true. That is, an allegation that Stewart has AIDS is consistent with an allegation that she was HIV-positive, but not vice versa. If a person has AIDS she is necessarily HIV-positive; but a person who is HIV-positive does not necessarily have AIDS.
(footnote 3). In the kind of logic I was taught, "consistency" between two propositions means that it is conceivable that both can be true at the same time, or (more syntactically) that assuming both will not let you derive a self-contradiction. This is a symmetric notion. It makes no sense to assert that A is consistent with B yet B is not consistent with A.

I wonder whether there is a particular legal meaning to "consistent" which is different enough from the logical one to make the above quote senseful.