Okay this makes more sense.
You are saying it is not enough to show that transitions/transversions deviate from uniform, we also have to show that this is positive, or beneficial, leading to more successful mutations than would take place with a uniform distribution.
In the case of transitions/transversions, actually, we know that this is the case. Transitions are more common, and are more likely be beneficial than transversions. That means that the transition/transversion imbalance skews mutations to beneficial ones, much more than we would expect from a uniform distribution.
That makes them “active” in your terminology, right?
Well, as I think I’m showing here, transitions/transversions would be more successful than uniformity, so they would triger the detector. Is that a good or bad thing from your point of view? I don’t know. From my point of view that’s a bad thing.
Yes, I know what you are talking about, and if that is your point I agree with your intended meaning (though I do cringe at the use of “random” in this way). Strictly speaking, mutations are not independent of fitness in important ways (but they are still technically random), and are often biased towards fitness. One such example is the transition/transversion imbalance, which skews mutations towards beneficial (or at least less harmful) changes to proteins.
I don’t think that Larry Moran would disagree with my intended meaning here. If I am understanding @johnnyb correctly this has to do with a real wart or imprecision in how biologists often talk about “random.”