I agree. Incidentally, although you probably already know this, Cultivars aren't necessarily created through artificial breeding. Some occur naturally and are maintained under cultivation thereafter.

As for why the lyricist chose that name, it's probably just the name he heard when he saw the flower in 1850s and asked, "What is that?" Obviously, "aronatus" never caught on. The eventual common name that stuck was the more mundane "blue-eyed wildflower tulip" or just "blue-eyed tulip." Perhaps "aronatus" was a name used locally at the time that was never recorded, or perhaps he just made it up as a more "botanical" sounding name that would scan within the song. As you say, we'll probably never know. On the other hand, here we are 150 years later and we're still learning things, so who knows. Not every old botanical journal has yet been copied and indexed on Google books.