The story of The Hangmen is very confusing and I'm not going to try to explain it all here. This is the quickie version. Once upon a time there was a surf band that called themselves The Reekers. The Reekers put out one bitchin' instrumental record in 1965 called Don't Call Me Flyface with a Flip-Side of Grindin'. That was released on the tiny Baltimore soul label of Ru-Jac Records. Both songs were composed by band leader, Tom Guernsey. It got enough air-play that it gave The Reekers a glimmer of hope. The Reekers then recorded two more Tom Guernsey vocal originals (this time with band member Joe Triplet singing) at two different times at two different studios. Shortly after recording the numbers, singer Joe Triplet and another member of The Reekers went off for their freshman year of college.
So here was Tom Guernsey shopping two demos by a band that no longer existed. Around this same time, Tom and his brother John Guernsey agreed to join a local upstart band called The Hangmen. Monument Records bit on the demos that Tom was shopping and someone, perhaps Tom, decided to release it under the name of his new band, The Hangmen, even though it was members of The Reekers playing on the record. What A Girl Can't Do became a minor local hit when released at Christmas time in 1965 and Monument pushed The Hangmen into a studio to record a full length LP. The problem was that The Hangmen on the LP and on the subsequent two singles was largely a different band - with a different singer -- than on their hit record. Clear as mud, right?
The picture below is of The Reekers, the band that actually recorded What A Girl Can't Do. But Joe Triplet is not in the picture. Tom is in the middle. The pic was lifted from the good folk at Garage Hangover.