A gap around the pickup will not affect the tone. Why would it?
All you really have is a small gap between the two screw tabs on the bass side.
If you look at some basses with the pickguards removed, you can see a big rectangular rout around the pickup that you don't see with the pickguard on. The size of the pickup rout has nothing to do with how the pickup works.
I think he was referring to placing the pickup in a particular POSITION to minimize the gap, would affect tone, which it likely would.
J