"Her little Scotch song."

All that might mean is that he'd heard her sing it several times before (which seems likely since he writes that he'd sung along). But perhaps she sang it mainly on the stage in Scots character. We don't know. We can't just assume that he'd heard other versions.

Perhaps Mrs. Knipp simply told Pepys that it was Scots. Who knows why she thought so? Did she learn it from a Scot? Was it a groundless assumption? Or perhaps the song seemed to be "Scotch" because it was set in Scotland. Without Mrs. Knipp's text, we can't know. Can we even be sure that she didn't write it herself? After all, it's "her song."

I don't believe we can draw any conclusions at all about the song from Pepys's passing note except that Mrs. Knipp sang it more than once and that Pepys liked it.

Though it is certainly quite improbable, Mrs. Knipp's song may not even have been Child's ballad: just consider the recent thread on two quite different songs titled "The Rose of Tralee," both of which appeared within a few years of each other.

Ballad characters are so briefly sketched that their "real" motivation and psychology are mostly rooted in the imagination of the singer. (Example: Could Barbara have been a lesbian? Sure, why not! Or maybe the hapless pair came from feuding families! That would really be cool!)

The psychological analysis of fictional characters is very much a 20th C. development. It is not one that appeals much to the traditional singer, who doesn't usually have a degree and is more interested in action than in analysis. ("He loved her and she coldly rejected him as he was dying, but she regretted it and after death we got a supernatural indication that their souls were linked." That summary, sometimes including its implication that true soulmates may do fine after death no matter what happened in this life, seems to me to cover 99% of what the lyricist, Mrs. Knipp, Pepys, Child, and most singers since then thought about it all.

Another possibility for the basin of blood: sick from unrequited love, "Jemmy" was simply being leeched to balance his humors. I believe that would not have been unusual for the time. In that case, as most people have assumed, he really was dying of love rather than of some infection.