There are Greek bits that fit into H2, but they’re either much smaller bits, or reflections of the text in later chroniclers, rather than self-standing witnesses like the Madrid ms and the Latin Barbarus for H1, or the Books of Generation and the Armenian version for H2.

The short answer is that there are greek fragments of H2 and that it is likelier that they stem from the H2 “recension” rather than stemming from a retranslation of an inexact Latin translation. Of course “likelier” is the key word here, many things are possible, but I think that the current theory makes the most sense.

Or is this simply a convention I don’t understand?

Quotations by heretics appear in all the catenas, especially often extracts from Apollinaris. But the words indicating author often drop out of catenas, even when quite orthodox. It is most likely this is the reason for the confusion. We have no real evidence of anyone reading Papias directly at this date, so it seems unnecessary to suppose it. But we know that Papias was extant in the times of Eusebius, ca. 320. Apollinaris was active ca. 360 in the reign of Julian the Apostate, so he could easily have had access to the text.

I suggest, therefore, that early catenists like Oecumenius are responsible for transmitting a passage of Apollinaris, which contains the words of Papias, and is copied thereafter in shorter or longer forms, depending on the damage caused by loss of author symbols on the copies.