If you look at the Metal flowers within the menu, you see that they have various bits of poetry connected to them. I've seen a number of people wondering why that is and that's because, in short, the scientist behind DEMETER was a huge poetry nerd. I believe they either coded it in somewhere and when DEMETER went rogue with the rest it pulled the data, or maybe Gaia learned and absorbed the knowledge. The how is a little fuzzy, but there's no more APOLLO to have drawn this cultural knowledge from so I think the primary tie is the DEMETER scientist.
How do I know? Well at the end of the game one of Sobek's journal entries touches on it. Shown here. The entry mentions both Longfellow and Tennyson by name. There are two different Longfellow poems (Flowers and Nature) included in the flowers, and one Tennyson poem (Farewell). There's also a lot of Thoreau. So a bunch of poets who love nature. Again, not sure if the scientist coded this in, or if DEMETER grabbed poems related to nature on its own. We also know that they talked about DNA as a storage device, so maybe that has something to do with the flowers having information in them. Maybe that's how APOLLO information might have lived on, within DNA?
TL;DR : The flowers share nature poetry because the scientist that wrote that subprogram was a poetry nerd and probably passed it on.
I just thought this was really cool and wanted to share it with you all.