I don't know. I sort of pictured one complaint bringing the investigator to town, who then would walk in and out of stores, restaurants, etc. just to see what he or she could hear in the other establishments. I'm also assuming that in major cities (NY, LA, Chicago), there was probably someone there year-round just making visits.
The people I talked to said that one day a guy just showed up, asked them what radio station that was, then asked "do you always play it in the store, or do you listen to other stations or play recorded music, too?" Next question would be "how long you been doing that?" and then out would come the business card, and a brief conversation about becoming a licensed establishment.
If there wasn't an immediate agreement to become licensed, that's when the strongly worded letters would show up.