Maybe I am but I also think the explanation still isn't right and is highly dependent on the game. You aren't 'texturing' 2D assets in renpy, it's a picture. It's already been' textured' in other programs prior to hitting renpy, all renpy is receiving is a screenshot of something.
Now depending on the game, the background, characters etc may all just be part of one image. This is how Ecchi Sensei does it, he builds the characters in Illusion's PlayHome software, environments (or built in unity and ported into PlayHome) then they are placed for the scene in 3d space (since it's all 3d models) and screenshotted > picture into renpy. Some times picture animations (or videos? Not sure BlueCat does actual videos).
Other games may separate the background, characters etc into separate images and overlay them to reduce game size bloat or other design reasons, just a different way of doing it but when done wrong makes characters feel detached from their backgrounds.
Taking screenshots is essentially the extra step here, and as you said it is indeed highly dependent on the game. Some concepts would be easier to pull off in 3D than in 2D in vice versa.
As far as I understand, he was quoting a friend, and that friend was only talking in general terms (and definitely not in terms of ES). Hugely branching paths would indeed make designing every scene and taking out renders for each a real headache, and as mentioned in the original quote would make it harder to go back and change things as you would have to consider multiple branches.
And as you mentioned it isn't exactly true in the case of ES as the story is mostly linear (you choose to see/or skip things) and there are essentially no real branching paths here.
I am not saying you are wrong, I just think you missed the point of the OP in being that it indeed can be hard to change up things in a branching story (compared to a linear one).
I think it mainly just comes down to the game's design, you could have equal tediousness in a fully 3d game that had branching actions as well. 3D games that let you walk around have more things to consider and potentially fix compared to a Renpy game where every action is fully controlled and directed.
I agree entirely, it is at its core down to the design decision. Because of this point only, traditionally, 3D games would be largely linear, and 2D games would use branching paths.
I guess mainly I think calling it a 2d game while technically correct simplifies how it's made too much imo.
For all intents and purposes, renpy games (like the ones we are talking about) are indeed 2D games that have 3D CG. Having 3D CG doesn't make the game a 3D game. Again HS (or PH) is a 3D game, but ES (other similar renpy games) are 2D. HS is being used as a tool to produce 3D graphics for a 2D game. So again in the context of the original conversation, I would like to stand on my point that it (the ES like renpy games) are 2D games. They do use 3DCG from a 3D game (Illusion titles) but they are still only using pictures (as you yourself pointed out) from these games, making them technically and rightfully 2D.
The tool in this case is a 3D game in itself is beyond the point I believe.