Actually true. Turing was still a big deal among computer hobbyists in the 60s/70s. Today he's largely forgotten. Early interviews with Jobs and Woz reference the logo to Turing, but then they backed off that story in later years.
Better let the newbies in on the joke. Alan Turing committed suicide by injecting an apple with cyanide, then having a bite. He was a sodomite in legal trouble looking for a way to spare his mother's feelings.