Does DN2 and MN36 provide an irrefutable statement on the fact of rebirth?
In response to the comment of Ilya Grushevskiy

Rebirth has everything to do with the Buddhist soteriology because if it weren't for rebirth suffering could have been easily ended at natural death or at any moment "in the here and now" with suicide, and the entire teaching if the Buddha would be pointless and vain.

But it is because of rebirth that beings need a method of salvaging themselves from suffering, propagation of which was the purpose of the Buddha's ministry.

It is exactly because of rebirth that liberation must be attained here and now, otherwise next birth follows.

The stock phrases are not to be dismissed, it's agreed that they actually constitute the core of the Dhamma. Besides these stock phrases there're many suttas which deal with destinations for next existence based on the behavior in the current life.

Secular Buddhism is a cherry picking Buddhism, its proponents only select what conveniently fits in with their preconceptions rooted in Western rationalism, discarding the rest as 'superstitious'. They don't seem concerned with samsara and ultimate predicament of existence, they're happy enough to alleviate some suffering in this life using the Dhamma as a psychotechnic. But this is not exactly the gist of the Buddha's teaching.