This only happened a few times while I was on the radio in the early to mid '90s, but it was a few times too many. Listeners would call and ask, "Do you know a song that goes...?" They would then sing a lyric or two from it. If I didn't know the song, they'd say, "Well, could you find out and call me tomorrow (or next week) at...?"
"Sorry, but no," I'd tell them. I didn't want to set a precedent of calling strangers with the names and artists of songs I didn't know.
Today, fortunately, in a time of easily accessed song lyrics and apps that identify most songs, that problem has largely vanished.