"I also have seen the suggestion that "greensleeves" was a nickname for a promiscuous girl (grass stains on her sleeves)."

Take it from a girl - if you do it on the grass, you don't get up with stains on your SLEEVES.

Why is it that some people have to turn every woman mentioned in literature into a whore? Reading Mudcat threads, we hear that Sweet Molly Malone (who was imaginary) is The Tart with a Cart. We hear that the woman in Raglan Road was a prostitute, though there's no evidence for that. Now Greensleeves is a slut.

Give it a miss!

I stand my my slieve theory, above.
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As for Henry VIII's supposed authorship, the main reason for discrediting it is that there are no contemporary references. If an autocrat like Henry had written a playable song, his courtiers would have fawned, doted, lavished praise and recorded it in all their diaries. It would have been in all the newspapers, had their been newspapers.

I for one am glad that he has no connection to this beautiful song.