it's not "the philosophy of positive reinforcement" that creates issues. the philosophy is to reward what you want (VS punish what you don't want, VS remove punishment when they do what you do want VS remove good things when they don't do what you want). IF they reward barking then YES they are cuing that behavior and encouraging it but that isn't because of the training philosophy. it's because of what the trainer is rewarded
I would be honest that it's not much of an issue at home so it's something about that environment (likely much more high energy and more stuff going on) or how they reward (what they have maybe accidentally rewarded) that is causing the issue. I suspect it's the environment. so hard for you to work on that other than practicing her in other busy busy environments that bring her to that level.
please just don't blame "positive reinforcement" for causing the behavior. Positive reinforcement is NOT "treat treat treat". it's marking and rewarding the behavior you want, the behavior you want repeated. Rewards, once a behavior is learned, should be phased out. once the dog knows you move on from the "training a new command" phase and either into proofing (they know to do it in all times in all places - here you are still in training so would reward, then phase out again) or to just keeping the behaviour (here you would not reward reward reward - you may randomly reward just to keep things fresh but it should be sporadic and unexpected).