Does DN2 and MN36 provide an irrefutable statement on the fact of rebirth?

Some Secular Buddhists and some members of Buddhism.SE do not accept that "Rebirth has always been a central teaching in the Buddhist tradition" (according to Thanissaro Bhikkhu in this essay ). They usually interpret this as something else, e.g. rebirth in the animal realm, as momentary animalistic states of mind etc. In my view, the DN2 excerpt below, provides an irrefutable statement by the Buddha on the fact of rebirth. A very similar statement can be found in MN4 , MN36 , MN19 , MN119 , SN12.70 , SN51.20 , AN9.35 , AN5.28 , AN3.100(xi-xv) , DN1 , DN12 and KN (Iti 3.50 ). This statement can be found in all the five nikayas. MN36 is said to be one of the earliest suttas by Thanissaro Bhikkhu . Questions: 1. How could this be interpreted in any other way? 2. Or do Secular Buddhists doubt the accuracy of the translation of this sutta and all the other referenced suttas? 2. Or do Secular Buddhists doubt the authenticity of this sutta and all the other referenced suttas? > "With his mind thus concentrated, purified, and bright, unblemished, > free from defects, pliant, malleable, steady, and attained to > imperturbability, he directs and inclines it to knowledge of the > recollection of past lives (lit: previous homes). He recollects his > manifold past lives, i.e., one birth, two births, three births, four, > five, ten, twenty, thirty, forty, fifty, one hundred, one thousand, > one hundred thousand, many aeons of cosmic contraction, many aeons of > cosmic expansion, many aeons of cosmic contraction and expansion, > [recollecting], 'There I had such a name, belonged to such a clan, had > such an appearance. Such was my food, such my experience of pleasure > and pain, such the end of my life. Passing away from that state, I > re-arose there. There too I had such a name, belonged to such a clan, > had such an appearance. Such was my food, such my experience of > pleasure and pain, such the end of my life. Passing away from that > state, I re-arose here.' Thus he recollects his manifold past lives in > their modes and details. > > Just as if a man were to go from his home > village to another village, and then from that village to yet another > village, and then from that village back to his home village. The > thought would occur to him, 'I went from my home village to that > village over there. There I stood in such a way, sat in such a way, > talked in such a way, and remained silent in such a way. From that > village I went to that village over there, and there I stood in such a > way, sat in such a way, talked in such a way, and remained silent in > such a way. From that village I came back home.' In the same way — > with his mind thus concentrated, purified, and bright, unblemished, > free from defects, pliant, malleable, steady, and attained to > imperturbability — the monk directs and inclines it to knowledge of > the recollection of past lives. He recollects his manifold past > lives... in their modes and details.