You didn't understand me, I've just confirmed that DNS servers in System > General Setup are not XMLRPC synced by design. Of course we sync XMLRPC everything:)
The issue is fixed. You were right when mentioning ISP. I've contacted them and it turned out it was their fault. They have had a route which routed all traffic to WAN VIP address, even though we are directly connected. So, all the replies for traffic sent from backup box WAN address, were sent to WAN VIP owned by primary box.
The only weird thing is that ICMP traffic was passing (ping, traceroute -I), UDP was passing partially (DNS lookup, drill), and (I think) TCP wasn't passing at all (couldn't telnet to any site port 80 from backup box).
Thank you, very much. You were of great help!