But the Arunta had not made totems hereditary, but accidental, so all the children of one crowd of mothers were placed in division A, all other children in division B.The mothers in each division would have children of all the totems, and thus the same totems now appeared in both of the exogamous divisions.

If a man married into his lawful opposite class, the fact that the woman was of the same totem made no difference.
I have offered quite an opposite explanation.

Arunta totems were, originally, hereditary among the Arunta, as everywhere else, and no totem occurred in both exogamous divisions.

The same totems, later, got into both divisions as the result of the later and isolated belief in reincarnation PLUS the sacred haunted stones.

That superstition has left the Kaitish PRACTICE of marriage still almost untouched.