I tweeked the dhcpd daemon as much as I could to coax the clients into thinking it the DHCP lease came from the same machine as JRec, but to no avail.
It really shouldn't matter where the DHCP lease comes from. On my network here I've used the DHCP server built into my Linksys router as well as a DHCP server on my Linux box (which is a different machine from the music server) and never had a problem with either.
The only idea I can come up with now is that the DHCP server isn't telling the Receiver the correct addresses for the gateway or the DNS server. As long as your Receiver and server are on the same network the gateway shouldn't matter. As for the DNS server, everything is done with IP addresses inside the Rio however RioPlay does do a "gethostbyname" on the IP address returned from JReceiver. I don't know if that causes a DNS lookup or if the resolver is smart enough to recognize it as an IP address and just return it.
Do you have other devices on your network using DHCP?