It has occurred to me that perhaps some of the confusion regarding why support profs should get 80% checks on pistol perks, while advs should have 100% checks, comes from a general ignorance about how weapons work.
"Advs are pistol experts, they should use them the best!" you say.
Right, well let's take a closer look at how pistols actually work and see how that claim pans out.
1. Weapons have a main AR, this determines how often you hit and whether perks land.
2. Weapons with specials also have a specials AR, determined (loosely) by the amount of skill you have in the weapon special (fling, FA, burst, etc), and this determines how well specials hit.
3. AS works on a multiplier system.
As it turns out, in an average endgame setup, advs. have:
1. More main AR. (Support profs must sacrifice a lot to compete here).
2. More specials AR. (Not even a competition here, really).
3. A higher AS multiplier, and at less of a sacrifice.
So as you can see, advs. WILL out perform support profs wielding the same weapons in a similar setup, even if advs have 100% checks on perks and support profs have an 80% check.
On top of that, advs have a far superior AR template (this effects how much extra damage you get for additional AR after 1k), and they have more add damage in general, which also significantly boosts how well their pistols perform.