Then the sentence in #14 saying this: “This means one is essentially an Anāgami by the time one is fully absorbed in the first Ariya jhāna”, should be read with this logical order:
IF one is fully absorbed in first Ariya jhana THEN one is essentially an Anagami
But that not implying the other direction:
IF one is essentially an Anagami THEN one is fully absorbed in (first or an) Ariya jhana
That last sentence is what I erroneously interpreted.