Wade in the Water (1970) by Willie Mitchell. The version embedded above is an instrumental. I didn't hear that part of the radio show so don't know if this is the version she played.
Mitchell was born in Mississippi in 1928 and grew up there but moved to Memphis in high school. Wikipedia describes him as "an American soul, R&B, rock and roll, pop and funk record producer and arranger." His website has an informative obituary and says,
Constructed as a theater in 1915 and converted into Royal Studios in 1957, Royal Studios, home of Hi Records and the Hi Rhythm Section, grew from a minor rockabilly studio into one of the most successful producers of soul music worldwide.He was 81 when he died in Memphis in 2010.
Willie Mitchell pioneered the Hi Records signature soul sound at Royal Studios...