When you want consistency for the sake of development (i.e. when new features are implemented on another platform, incorporating them across the board is easier and faster) then I say go for it.
I get the copyright holders’ point but they aren’t going about it any differently than a big name company. Is this the whole story? The source article states that they filed a suit without any mention of them trying to contact WB beforehand. Plus, Scribblenauts doesn’t advertise those memes in the game so I’m not sure where they got that idea from.
The menu concept looks great! Do you think the branding needs to be there? One thing that stands out on the tumblr app is that you instantly know it’s a tumblr app without it saying as much all over the screen. I think Facebook is pretty ubiquitous and could get away with it in their app as well.