It's Laravel's missing implementation of phpseclib's ssh-agent that requires that many information for establishing a SSH connection.
That's why Rocketeer does not allow to rely on the ssh-agent next to username/password and privatekey/passphrase authentication as does Capistrano.
A proposal was stated and merged to include phpseclib's undocumented implementation for using the ssh-agent instead of an explicit key.
Rocketeer would profit from this as it relies on said implementation of phpseclib in Laravel.
(Thanks to @hannesvdvreken, @ThomasPayer and @passioncoder for pointing in the right directions)