I discovered that if I disabled the Long Press action in Pressy (mine was set to toggle Mute), Touchless Control can stay enabled.
BUT -- with Pressy plugged, the MotoX no longer responds to the "OK Google Now" voice command. Apparently, with Press plugged in, the MotoX cannot detect a microphone from which to receive the voice commands. If I unplug Pressy, it works fine.
This is also apparent when you try to "train" the MotoX to use your voice for "OK Google Now" in Touchless Control. If you attempt to train the phone, Touchless Control says it cannot detect a microphone and asks you to plug in a headset.
For those people using credit card readers on the MotoX, does the "OK Google Now" voice command work with your device plugged in?