Shit, you're probably right. It only worked because I didn't tell SSH to only use the specified identity files (I threw it together in five minutes without really testing it, you can forgive me). Changing one of the lines to this (which it should have been all along):

    GIT_SSH_COMMAND="ssh -i $KEYFILE -o IdentitiesOnly=yes" git "$@"

...comes up with "Permission denied (publickey)". So, yep, you're 100% right.

Oh well. There's still HTTPS!