Well, the theist wouldn't agree that she's committed this fallacy because she instead has a double standard. Everything that exists naturally is contingent, but all of these things must derive from something supernatural which is necessary or metaphysically independent.

The problem is that this double standard defeats the point of theistic arguments. The argument about contingency is an expression of reason, and there's no reason to think that reason applies to anything beyond nature.

The theist has to say, then, that reason, consciousness, and freewill are supernatural, so we can see beyond the apparent universe to our ultimate home (in heaven or hell, I suppose).

Still, if there are two realms, and reason belongs in supernature, why use reason to understand nature? There should be two cognitive methods (faith and reason, say), one for each realm.