Payment channels are similar. Nobody has your coins but you. Yes, they are in the channel. Does that allow you to doublespend them as to practice fractional banking? No.
This notion seems to be at the essence of the disagreement. I think you are saying that coins in the channel are not vulnerable to any kind of mischief, and that "the channel" is not a centralized entity. Is that a fair representation?
Edit: I'm not up to any kind of "gotcha" trickery with my question - just trying to understand. The next step would be to try to throw extreme cases at the model and see if it can handle them, but first it's important to understand the model.