I've not heard of it as a "standard" practice, but an AM radio channel has a pretty narrow frequency band, and you can only broadcast (or receive) rather "low-fi" signals. It is conceivable that some bands - or some stations - may have felt they got a better sound by tuning "off" a little one way or the other.

On the other hand, he may have "discovered" someone on the radio that he could play with by retuning, and made his own conclusion that it was a "practice." My own AM-radio-days experience at trying to play along with the radio indicated that most broadcasts were not in "concert pitch" tuning, but I never found a consistent change. The explanation I got - mid '50s - was that the recording studio sometimes shifted the tape speed to get what they wanted after the players went home - and before they put everything on the "master tape." Sometimes up - sometimes down. I doubt that the "authority" for that explanation was actually knowledgeable, though.

Before electronic tuners became common, it was often the custom to "tune to the piano," and it was not unlikely that the nearest piano would be tuned to "standard pitch" rather than to "concert pitch." "Standard pitch" is a little more than a half tone lower than what we normally use now. It doesn't make much difference for an "all-strings" band, but if you have an accordion or flute in the group, you'd have to "tune up a half tone" because many "concert instruments" can't satisfactorily tune down to "standard pitch."

This is all speculation, of course. It would be helpful (or just interesting) to know if your dad actually played in radio sessions - and when/where, and perhaps what your reference for "standard tuning" was.

John