Very true
It's still an akward definition for a planet though, what if Charon had been in an eleptical orbit, so the barycenter would sometimes be inside, and sometimes outside of pluto, would charon change planet-moon status during it's orbit?
The whole double planet thing seems unnecessary, just name the heavier of the two objects the planet and the lighter one the moon, you're unlikely to find two bodies orbiting each other with exactly the same mass. If you do, just dump a couple of tons of material on one of them and your problem is solved.
