No idea why she didn't have a recoil pad. ISSF skeet is a low-gun game so perhaps it was removed to ensure a smooth mount or any of several other reasons. The important tuning would be fit, trigger pull, weight adjustments, barrel tuning for pattern consistency and most importantly barrel regulation which can vary widely among entry-level Berettas.
Shooters who are sponsored shoot whatever model of gun they are given by their sponsor and it makes sense for Beretta to give her a gun that looks like one you could buy off the shelf.
FYI, according to this she did not shoot a 686 but a 692 while the other team Berettas shot the DT11.
http://www.beretta.com/en/world-of-beretta/team-beretta/2nd-issf-world-cup-2016-skeet/