During the installation, the IP address of the only network interface has been used. Basically, the setup.py script was left to use the IP address it detected. That IP address was apparently used in 3 places:
1) HTTP -- port 80 -- VirtualHost directive in Apache config.
2) HTTPS -- port 443 -- VirtualHost directive in Apache config.
3) /etc/hosts where that local IP address is mapped to the hostname specified on setup time.
Replacing 1) and 2) by "*" works pretty well, apache correctly listens on one and only interface, even if local IP changes. Anyway, removing mapping from /etc/hosts causes the problem described, even if IP stays the same.
Please note that our Elastic Load Balancer is configured as "TCP", so it passes plain TCP traffic through it, it is _not_ configured as HTTP(S) "man-in-the-middle". In another words, any traffic sent directly to local IP address should be pretty same as if passed through ELB.