While this is a very nice canyon, Enigma is not a viable escape from Muddy Creek back to the rim. The "stopper" upclimb is only 300' or so from the creek, so you can check it out for yourself. Maybe conditions have changed in recent years. Our party of three experienced climbers did not feel that the upclimb was safe to solo.
From recent reports, I don't think it has changed much, but the upclimb is ~5.7, making it fairly challenging. I've upclimbed it with and without a rope, but "safe" is a relative term. There are certainly penalty points for falling.
The canyon isn't really presented as being an escape from Muddy Creek to the rim as there are less technical ways to do this (i.e. Poncho Wash).
It does say the following:
Option #1: The first option is to ascend back up the canyon the way you came. Of course to do this, you may have to leave ropes behind at every drop, and you may have to use mechanical ascenders. If you are confident with climbing 5.7, you can upclimb all the drops, as we did in April 2007.
But, that's only presented as an option if you had already descended the canyon.