Last one, I promise. Sorry for all the messages. Another interesting behaviour is that it doesn't do it consistently to "similar" faces. For instance, in this slightly more complex shape than the first: notice the blue surface is triangulated, but the red one isn't. I like the red one ;) Though it still has the midpoint subdivision as above.

Part of this feels like a sort of hidden "divide larger than" limit. At least the midpoint division thing...sorta...