Since a standing wave is an interference pattern created by traveling
waves, having 'only standing waves' would obviously be an impossible
circumstance.

By "only standing waves", I meant pure standing
waves and nothing else.

We've been through this one before. If the SWR
is 1:1, there is only a forward traveling wave.
If the SWR is not 1:1, there exists a forward
traveling wave and a reverse traveling wave.
If the SWR is infinite, the amplitudes of the
forward wave and reflected wave are equal and
a pure standing wave is the result.

"Only standing waves" doesn't mean the underlying
traveling waves don't exist. It simply means that
the amplitudes of the forward wave and reflected
wave are equal and therefore all of the energy
components in the traveling waves have combined
into the standing waves.

For instance, a lossless stub would contain "only"
standing waves, i.e. pure standing waves.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com