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Depending on the conditions, it is through that neutrinos can pass through even very degenerate matter like that which forms neutron stars. "Empty space" really doesn't mean all that much if the thing that is interacting with it does so weakly.

Does this mean a black hole is "full"?

100%

But visible light can't get through us at all. Does that prove that we aren't empty space? The whole point is that this criterion is incredibly ambiguous.

> But visible light can't get through us at all.

visible light definitely gets through me when I put my hand in front of a bright light source

Well, light passes through glass so transparency doesn't seem to be a credible measure of solidity.

I think you mean that solidity is not a credible measure of space being filled.