The description of D.O. that appears in the suttas certainly refers to the three lifetime model, as words like "Death" and "Birth" are pretty unambiguous:
These words are completely ambiguous, in our own culture and likely in every culture throughout recorded history.
"The passing of beings out of the various orders of beings, their passing away, dissolution, disappearance, dying, completion of time, dissolution of the aggregates, laying down of the body — this is called death."
"The birth of beings into the various orders of beings, their coming to birth, precipitation [in a womb], generation, manifestation of the aggregates, obtaining the bases for contact — this is called birth." - Sammaditthi Sutta
These words were written 300- 800 years after Siddhārtha Gautama's death (actual date unknown). It is entirely possible that this is a perversion of another use of "birth" and "death" by Siddhārtha Gautama. There is no easy certainty there.
There's nothing ambiguously metaphorical about it either. Bhikkhu Bodhi pointed out, in his discussion of this Sutta, that when the Buddha spoke in metaphors he was usually explicit about it. We tend not to find anything metaphorical in the Suttas without the Buddha either saying "this is a metaphor for such and such" or using phrases "like" and "as."
But who actually wrote it? No one has any realistic idea. Some scholars aren't confident that there are any or much of Siddhārtha Gautama's words in the teachings. So let's go to the beginning - the 4Nt, which is startling clear and contains no mention of literal rebirth. If literal rebirth was so central then the logic stream would dictate this:
Birth is suffering, aging is suffering, illness is suffering, death is suffering, rebirth is suffering.
Birth is suffering, aging is suffering, illness is suffering, death is suffering.
There's no mention of this supposedly critical piece of information at all, which would have unambigiously supported the notion of cycling endlessly through repeated lives:
birth is suffering, aging is suffering, illness is suffering, death is suffering,rebirth is suffering, birth is suffering, aging is suffering, illness is suffering, death is suffering,rebirth is suffering, birth is suffering, aging is suffering, illness is suffering, death is suffering,rebirth is suffering...and so on
The very experience that theoretically creates the cycles of existence is glaringly missing. How can this be accounted for? It's unlikely that it is just an error of omission on the part of Siddhārtha Gautama.
Some people engage in mental hula-hoops in an attempt to squeeze literal rebirth into "Right View" in the N8FP, being aware of this glaring break in the logic stream...but that's quite an unrealistic reach:
And what is right view? Knowledge with reference to stress (dukkha can also be translated as suffering), knowledge with reference to the origination of stress (or suffering), knowledge with reference to the cessation of stress (or suffering), knowledge with reference to the way of practice leading to the cessation of stress (or suffering): This is called right view.
...because there's no mention of it there either.