"Samuel Pepys, in his 17th century diary, was aware of its singing in England;"

and where did that information come from? Presumably the author of your website got it from the introduction to Barbara Allen in Child (vol II), in which he says: 'Mr GF Graham, [in] Songs of Scotland...has pointed out an allusion to the "little Scotch song of Barbary Allen" in Pepys' Diary, 2 Jan 1665-6'

So Pepys actually calls it a Scottish song.


"the more-interactive web may, in some cases, be more accurate than a published book...?"

Book or website, what matters is sources and provenance. There are far too many websites out there which don't cite sources, are plagiaristic, or are wholly factually inaccurate.

As I used to say to my first-year university students: Just because you saw it on a website, that doesn't make it true. As with books, it's about the quality and the integrity of the source.