But the herb was used in religious ritual, so I'm inclined to credit the nursery rhyme to a certain extent. Several nursery rhymes have odd histories.
Rue means "regret"--it was also the most effective flea repellant of the renaissance, which means it really wasn't that effective. Nicotiana was used from the New World as an effective mothball additive to linen closets, however.
That book also notes that much of the "odd histories" of nursery rhymes stem from a single book written by what would have been called a tinfoil hat guy today, except it was a woman, IIRC some time in the late 19th century. She found arcane meanings, like King Charles's head, everywhere.