So from the headphone's perspective, "balanced" means nothing. One of the drivers from a pair of headphones doesn't "know" if it's being driven by a bridged amp, or one single-ended one.
I will admit, "faux-balanced" is not an accepted term, but I don't think "balanced headphones" is anything other than "mixing up words that mean nothing", either. I mean, turning that middle sentence in your post around, this one: you're saying that balanced headphones are the same as unbalanced headphones with separate grounds (what I would prefer to call returns). That's not truly balanced. That's the headphone equivalent of "dual monoblock" design, whatever the correct terminology for that is.