This reminds me of a debate I see on internet forums concerning the First Noble Truth. Is it defining dukkha? or is it describing what dukkha arises in reference to? For example, are birth, old age, sickness, and death themselves dukkha? or is it that an unawakened person experiences dukkha in reference to birth, old age, sickness, and death? If the former then Nibbana is the end of birth, old age, sickness, and death (meaning no more rebirth). If the latter then NIbbana is not the end of birth, old age, sickness, and death but rather only the end of suffering arising due to these things.
I don't mean for this to be debated here; I'm just noticing the similarity in argumentation. If sakkāya is defined as the 5 khandhas then that is one thing. If sakkāya arises in reference to the 5 khandhas then that is something else. Funny enough, in both cases it comes down to arguing about rebirth.
BTW, MN 44 does not discuss the Four Noble Truths at all. Rather it follows the same format as the Four Noble Truths - definition, arising, ceasing, way to ceasing. The Four Noble Truths are regarding dukkha. There are many teachings in the scriptures that borrow the 4NT format.