This council presents a source problem sharper than that of the first. It appears in the Theravada chronicles of Sri Lanka and in commentarial literature of the same tradition, and it is essentially absent from the records of the other early schools, which describe their own councils differently or not at all. A council of the whole order that half the order does not remember is a difficult object.
Ashoka's own inscriptions do not describe it. What they do contain is a short edict, found at three sites, warning that any monk or nun who divides the order will be made to wear white and put out of the monastery, which shows that the emperor concerned himself with monastic discipline and that schism was a live problem in his reign. That is real contemporary evidence for the situation the council story addresses, without being evidence for the council.
The most economical reading, and the one many scholars adopt, is that a school council of the Theravada lineage has been remembered as a general one, and that its account was shaped to establish that lineage as the orthodox continuation. That is not a charge of invention. It is how traditions ordinarily remember. The atlas holds the entry because the event is foundational to Theravada self-understanding and to the transmission of the Pali canon, and marks the disputed points as disputed rather than presenting one school's chronicle as the record of all.