This looks like a problem I'm having, but I'm not sure, for you did not provide information enough to compare the cases.
My trouble is this (with WinXP and FC3): every time I change OS after rebooting, the internet connection fails, because no IP address gets assigned to my DHCP client (in both OS's an IP address gets assigned automatically). And the DHCP clients of both OS's send different information to the server, so an IP address assigned to windows cannto be used by Linux. Only if you wait for the DHCP lease to end, the connection can be activated. (That is to say, "ifdown eth0" and "ifup eth0" does not release the DHCP lease information).
Changing these remarks (intended to partially answer your question) into new questions for this thread:
1. Can I force Linux to use the IP address assigned to Windows? Or: the physical MAC address (which seem to be different as well)?
2. Can I make both OS's release DHCP information before shutdown automatically?
NB: it seems to me that the RedHat documentation says little about dual-boot problems like this, or did I miss anything?