Thanks, Karsten.
I should have mentioned, though, that the user is opening the form in the InfoPath client. The form was not designed for the Web. I know that IE's settings sometimes touch things in ways that aren't readily apparent, but would this still interfere in this case?
Also, I just learned from the other user that they're able to open "other forms" just fine. I've asked for clarification regarding the source of those other forms (ours or the other org's).
If the form was originally published to our network, would I have to have the user (or the local IT support) republish the form to a local network for it to be trusted there?