The requirement of vet always confused me if the jump height was already lowered by running skilled. For the description I will use the 16" P dog. If they are running skilled, they run ALL classes at the 12" level both jumping and non-jumping classes. This gives the dogs a bit of a time break in the non-jumping classes. However, the "vet" division does not allow for that.
Ok, now you have me confused, as to where you see an issue.

I have a dog who measures into the 16" class by a fraction of an inch. I prefer not to jump her nearly an inch over her withers, so I enter her in the Skilled category. That allows her to jump 12" in the classes with jumps, and I believe (as you say above) that she also gets 12" time in the non-jumping classes. Since she's only 4 years old, her *division* in all classes is Standard. (If your dog's not a Veteran, and you're not a Junior Handler or a Veteran Handler, then the dog is in the Standard division.)
When she becomes a Veteran dog, her category will still be Skilled for all classes. Her *division* for the non-jumping classes, as I understand the rules, remains "Standard" - last I heard, there isn't a veteran DOG category for those classes, only a veteran HANDLER category. So she still gets whatever time break she's been getting all along.
In the *jumping* classes, her division will be 12" veteran dog. As such, she will jump 8", and will get 12" Veteran times. Again, she'll still be in the 12" division, Skilled category, for the non-jumping classes - she gets the same time break she always did.