Not your screen monkey (he/him)
Well, you could be pedantic about the terms used.That defintion fails though against fire immune creatures and spells like fireball
Or you could make the realization that successfully saving means successfully resisting the effect to the best of the target's ability to do so. Being immune would also count as successfully resisting the effect to the best of the target's ability, though a save was not technically necessary.
I'd allow the character to use the beguiling twist in those circumstances.