The insurance company negotiates a rate for each provider, and you should get it regardless of which plan you choose.
Which was my point exactly. I get to pay the rate negotiated by my insurance. A high deductible plan has much less incentive to negotiate lower fees for everyday services, so potentially I pay inflated prices for these. I understand that some carriers have multiple plans, so those plans for that carrier will share the negotiations, but usually when I am choosing between an regular health insurance plan or a CDHP they are different carriers and different negotiated rates will apply. Further the results of these negotiations and hence the actual costs to me are not visible to me until after I choose and start to get bills for services.