A bit more Googling found the answer: it is a regression caused by a "fix" in Gnome to fix a reported problem where some individuals found it too difficult to create dual-monitor wallpapers. Apparently there are some patches available to the control-center package that will add a "spanning" option to the desktop background control, but Red Hat NAKed the change for 6.1. Apparently this is available in Fedora 12, but the option is missing in RHEL 6. See https://bugzilla.redhat.com/show_bug.cgi?id=616701 for the response.
I may try to rebuild the control-center RPM with the patches when I get some time. I'll post here if I make any progress.