Copper fill zones have separate clearance setting. (The settings in the design rules to not apply. Ok they might apply if your design rules have a larger clearance than the copper zone but i have not tested this.)
I see more of a problem with other tracks.
I think the nightly builds might give you more options there. (Again, i have not tested this personally. I use a very old nightly which has no new features in this regard.)
But be warned, the nightlies are unstable (or not guaranteed to be stable).If you use differential pairs they are incompatible with the stable release. (In other words: If you want to use the better features for diff pairs, you can not go back to stable until version 5 comes out.)