unless songs were learned orally a singer took a tune that fitted
Anybody who has spent an afternoon looking at the history of printed songs will be able to spot the flaw in this so-called assertion of fact.

A heck of a lot of songs started out as some kind of parody using an existing tune - the tune came first, and often the audience was meant to recognize it and react to the connotations it had acquired. (Jim Maclean is a master at that).   Getting printed or not was irrelevant at the point of creation, though it was mostly easier to get a song sung if you told the purchasers of your sheet what the intended tune was.

It gets interesting when a specified tune starts drifting away from the writer's original idea. Matt McGinn habitually did that to his own songs, so it wasn't always obvious what was being parodied by the time he first sung it. "Chi mi na mor-bheanna" drifted quite far and fast from its author's explicit choice, but the (undocumented) process was still an evolutionary one, not a matter of picking any old unrelated tune that "fitted".