From past experience I would have to disagree with you, at least on the "most often" part, Larry
Are you thinking that most people believe a rhizome is a kind of root? Or that they know it is a stem but call it a root anyway?
Edited to add, IMHO it is important to make the distinction because otherwise new daylily gardeners might think any piece of root left behind when digging up a daylily could regrow. Not all daylilies have rhizomes.