If I were doing a high number of transactions and relying on Stripe to provide all my CC processing, I would gladly pay an extra $25-50 a month to have priority support in instances where there may be fraud. Shoot, even at a couple hundred in transactions each month I would gladly pay for priority support. I would rather have a $25 expense each month than risk business loss due to real or suspected fraud. Shoot at some level I might even consider an extra nickel per charge to have a dedicated account manager who was always there for me and knew my business inside and out.
If you're putting a lot of volume though Stripe, all those things are possible.
Notwithstanding Stripe's SaaS-y "all pricing and deals are public" branding, they definitely have a BD team who can set you up with more direct contacts for certain types of questions, different rates than are publicly posted, and APIs that aren't public (to name a few things).