I see it as using a tune that's been used before, not lifting it. Sharing it. One result of Sydney Carter using the tune is that far more p[eople have become aware of teh song Simple Gifts than would otherwise have known it. (And he's always done his best to make people aware of where the tune came from, for that very reason.
Two different songs, each saying something different. Each has some qualities the other doesn't. It's a bit like a fiddle and a mandolin sharing the same tuning. "The mandolin has just stolen the tuning of the fiddle, and is nowhere near as fine sort of an instrument."