I am not sitting at a machine so configured, but glancing at the sshd man page I believe you have to trust RSAAuthentication for version 1 and DSAAuthentication for version 2 to do it.

This, of course, results in specific users on several machines getting automatic access to others, and means that a root exploit on any machine turns into user accounts on several. OTOH you stop having to have passwords sitting around in scripts, possibly passed in environment variables, and other such mistakes. Pick your poison. Personally I think it is worthwhile but I am no security expert.

BTW a good tool to use with ssh is rsync. :-)