"This video is not available" -- to me in New Zealand, anyway -- but I have this track, and it shows clearly that Mosely and probably Maxey were no strangers to gospel music. The song is a widely performed and recorded gospel standard (usually called I Thank You Jesus) and in the 1950s it became popular among gospel quartets. Two of the best-known groups to have recorded it are the Soul Stirrers and the Harmonizing Four; they and others -- I've just also spot-checked the Skylight Singers and the Southern Wonders -- used the loping swing that Mosely and Maxey use. There's no way of knowing exactly which group M&M modeled their performance on, but it definitely stems from an established quartet style; in today's lexicon this would probably be called a "cover".