Alert screencast viewer Stefano Bernardi notes that I missed a step at the end of the RVM setup in the Mac OS X/Linux Rails installation screencast. The first time you install RVM, you should put the line
[[ -s "$HOME/.rvm/scripts/rvm" ]] && . "$HOME/.rvm/scripts/rvm"
in the .profile file in your home directory (and then, just to be safe, log out of the terminal and then log back in). I've updated the screencast accordingly; sorry for any inconvenience.