I am familiar with the rest of the song without needing to read the lyrics. I see no contradiction between (on the one hand) the narrator accepting the parents' hospitality and playing them some tunes and (on the other) clearing off early the following morning.

We are not told why he departs so promptly – maybe he has an important commitment somewhere – but he does go on about the shawl (and about the girl's lack of embellishments) rather than about the girl herself, hence the speculation. Maybe he's uncertain whether to pursue the relationship both because of her prattling and because the shawl indicates that she's a widow. Is she a very recent widow with a baby on the way? Have the parents advised her to catch another man ASAP?

(None of this need be taken too seriously.)