ssh agent forwarding fails with "Could not open a connection to your authentication agent"

I'm posting this here because I spent a lot of time trying to find a solution using Google, reading man pages, and consulting a popular book on SSH, all to no avail.

The key to finding the problem was poring over the debugging output.

debug1: Remote: Agent forwarding disabled: mkdtemp() failed: Permission denied

The intermediate machine is a virtual server (RHEL 6.4) hosted by a cloud provider that uses an AWS stack. For reasons I can't explain, this is what permissions on the /tmp directory were set to:

drwxr-x--- 19  727  727  4096 Nov 28 05:30 tmp

Grep'ing through /etc/passwd I couldn't find a user with an ID of 727.

Correcting the permissions like so solved my woes:

sudo chown 0:0 /tmp
sudo chmod 1777 /tmp

Can anyone speak to the peculiar ownership of the /tmp directory?