Suggesting that this is a 'yes' or 'no' issue, does no justice to traditions of singing and reduces complex circumstances to a degree that is meaningless -
People sang (and still sing) for their own and other people's amusement, to pass the time when they're working at something and to express their creativity - and for all sorts of other reasons. Sometimes singers are paid and sometimes they're not.
Shantymen were paid to sing, it was the whole reason for their being aboard ship - but I don't think anyone would suggest that shanties aren't traditional.
When a wet nurse or nursery maid sang lullabies to the babies she had in her care, wasn't this part of her paid work? And did the same traditional lullaby and nurse become something different when she sang it to her own children to rock them to sleep and wasn't paid?
When Jos Mather, the Sheffield ballad-maker and singer wrote and performed his songs in the late 18th/early 19th century, he was paid. Other people sang his songs because they liked them (they were still singing them in Sheffield in the late 1960's) - I don't see that what Jos Mather and later singers did was different because some were and some weren't paid, I was just delighted to hear his songs still sung after almost 200 years.
At celebratory feasts in medieval monasteries, visitors to the feast joined in the refrains with the paid singer - and weren't paid for it. If you're just going to have two states - paid and unpaid - what happens when they occur simultaneously. Is one 'valid' and one 'unacceptable'?
And as for the idea that traditional song existed separately from the rest of culture for centuries,.....