Correct, as I understand it. No matter can travel at the speed of light, and no light can travel faster than the speed of light. But the rule doesn't extend to the rate of expansion of the "field" on which those things exist.
I vote we bring back “aether” as a valid term. The aether is stretching everywhere, and in so doing it spreads distant things away faster than light can overcome.
Yeah, ideas like this are usually called "tired light" models, they have been extensively explored for the last hundred years or so. A lot of these models have been shown to be false by experiments, but I guess if you try you can probably cook up models which haven't been falsified by anything yet.