That’s an EBT list, found at AN 8.52 and in the rule explanation of bhikkhu pacittiya 21.
The criteria are not actually that strict. Of course, if he is to instruct bhikkhunis, he needs to know their patimokkha, otherwise how can he teach and answer their questions?
And the rest of the factors are that he keeps the rules himself, knows many suttas–again, of course, otherwise he cannot teach–, that he is a capable teacher, pleasing to the bhikkhunis, that he hasn’t molested them, and that he has 20 years seniority. It’s kind of common sense that he needs these qualities.
In the early times, people were trained to memorize larger amounts of “texts”, as there was no writing. Learning patimokkhas wouldn’t have been such a big deal. Monastics do it regularly even nowadays.
For other tasks, the EBTs demand much higher standards. For example, to ordain someone, or to train a novice, the Anguttara Nikaya prescribes arahantship (see AN 5.251-3). That list was later watered down in the Vinaya, presumably because there weren’t enough qualified preceptors and teachers around anymore.