Hi Erika, 
Thanks for your feedback in the other thread. 
I’m minimizing my time on this discussion board at the moment, so won’t reply there for now. However, this question I felt like addressing now. So here’s my 2 cents. 
The quote from MN140, on the sage not dying, I think is interpreted in two ways, both of which I think are valid.
The first interpretation is according to the Buddha’s explanation that immediately follows. He says that the sage will not die because they will not be reborn:
The sage at peace will not be reborn, will not grow old, and will not die. […] For [Pali hi, indicating an explanation] they have nothing which would cause them to be reborn. Not being reborn, how could they grow old? Not growing old, how could they die?
That is, they won’t die again after they aren’t reborn. This is easy to understand, and it’s clearly one intended meaning, if not the main one.
(Notice that I translate “will not die” instead of “does not die”. The Pali present tense often has this sense of future/eternal truth, especially in terse statements like this, and I think in English this sense is better captured by using “will”. This slightly different translation may take away some of the potential confusion.)
The second interpretation is that a sage will not die because they have no sense of self. So from their perspective there is the death of the body (as it says earlier in the same sutta: “When my body breaks up and my life has come to an end …”), but there is no individual or person or “me” who dies. As it says right before the quote: “Having gone beyond all conceiving, one is called a sage at peace.” In other words, they don’t conceive that they are going to die. So this is another way—a less literal way—in which the arahant has gone beyond death.
However, to get to the heart of your question, in the second case ‘death’ still means actual physical death. It’s not the death of some kind of mind state, like certain momentary interpretations of Dependent Arising have it. So in either case it seems to supports the multiple-lifetime interpretation of Dependent Arising. That is to say, I do not see how this quote would support “rebirth in the present moment” as Ven Payutto calls it. Since the death in question is not a present moment death but a physical death, so is the birth in the same quote.
I also don’t know where the 2/3 and 1/3 division comes from. 
Your explanation may be right. But in either case, if one acknowledges that the standard 12-fold sequence is about actual rebirth, then at least the Nidāna Saṃyutta (SN12) is almost exclusively about that. Other main suttas on Dependent Arising (DN15 and MN38) are also clearly about rebirth, even though they present different sequences.
Perhaps the two people are just using different words but practically they are doing the same thing? (let’s say they both believe in literal rebirth) […] I’d be interested to hear what people think are the practical consequences!
It doesn’t answer your question, but I can say that the general practical consequences for other people was not a concern for me when writing the book. As far as I’m concerned, they will have to judge that for themselves.
But Dep. Arising is only understood by the noble ones. And problems will always arise when we think we are noble ones but we are not, when we think we have right view but we have wrong view. Then the whole path may actually be blocked, because we stop looking for alternatives. We think we already know and understand the Dhamma, but we don’t. 
Hence it’s good to have this in mind:
The fool who thinks they’re a fool is wise at least to that extent. But the true fool is said to be one who imagines that they are wise. (Dhp63)
In non-rebirth interpretations of Dependent Arising I have sometimes encountered the idea that stream winners may still have to take rebirth on faith, that they aren’t necessarily completely sure about it. This is wrong view, though. The core insights of the stream winner, especially the fruit, actually revolve around rebirth. That noble ones understand and have seen how rebirth functions, and that it involves no self (and that it can therefore cease): this exactly their insight into Dependent Arising (and Cessation). 
Hence contemplation of DA is said to be the “method of the noble ones” in the suttas. It is, crucially, not the method of the puthujjanas! 
This may be something to consider when some teacher say their interpretations of Dependent Arising are more practical, more applicable to daily life, compared to the traditional multiple-lifetime interpretation. Well, yes, they may well be! But that exactly defeats the point. Insights into DA are not those encountered in daily life. The noble trainees are solving a fundamentally different problem than the puthujjanas. They are the only ones who actually see the problem.
That said, as I also hinted at in the book, it may be that some noble ones just don’t have enough knowledge of the suttas to interpret Dependent Arising correctly on the technical/theoretical level. In some places sutta study is (or was, at least) actively discouraged, and the canon locked away in a glass cabinet. In such situations even noble ones may not have enough literary knowledge of the suttas to teach Dependent Arising in line with the Buddha’s intentions, even though they do have right view.
I hope that makes sense. Either way, it’s helpful to be able to tell apart theoretical differences of opinion from more fundamental ones. Because I think even two arahants will probably have some of those theoretical differences, since they exist on the level of intellect and not on the deeper level of view. (For example, explaining certain factors of DA in a certain way can be a mere intellectual difference or a skillful way of teaching. But the claim that stream winners would still take rebirth on faith, exists on the level of view.)
