It's frustrating addressing this crazy ass myth but no, it is not true that you don't have to cleanse your face in the morning. Yes, you cleanse in the evening, however don't think for a second that your face remains oil free, sweat free and dirt free throughout the night.
The skin repairs itself naturally while we sleep and, in doing this, produces dead skin cells and excess oil that need to be removed the next morning. Now don't go thinking a splash of water will help remove these nasties; water alone only removes around 65% of oil and debris from the surface of the skin. You will need a cleanser and I recommend using a gentle one, such as the La Roche-Posay Physiological Cleansing Gel 200ml (£12.00 Boots / £21.99 laroche-posay.us).