The reality is this is stupid and just leads to people working around the problem. Take for example corkscrew, which allows you to tunnel SSH over HTTPS proxies, without losing any of it's port forwarding or other juicy features.
If you feel like you really need to embarass them you can ofcourse run something like sshuttle over the top providing automatic VPN routing over this rogue SSH tunnel.
Worse yet they might install KeyBox on their AWS deployment because they don't have SSH outbound, which then promptly gets pwned because it's a relatively unproven Java web application rather than a battle-hardened unix staple (i.e sshd).
Corp networks and infosec departments are a joke.
In terms of auditing all you need to do is make proper use of *nix permission model and then enable sudo input/output logging and control access to sudo via LDAP groups. Send all of your sudo logs to centralized logging system like Splunk/ELK/fluentd/Flume etc.