Is the Airport set to forward DHCP addresses responses back towards the clients? Do you have the Airport in Bridge mode? Was the Airport ever set to offer DHCP? Are you seeing any messages on the Airport regarding double NATing?
What is interesting you said, that some Mac clients see private addresses. What is different about these and the Mac Clients that do receive the correct IP addresses? This may need further investigation.You may get additional info. when reviewing dhcpd.logs
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