"Yes. One could say something like "I know that you're billing me three times what you get from insurance companies, and I know that you'd pay at least 50% to a collection agency, so will you accept 40% now?""

Unfortunately, this misses another pertinent point, that the provider/facility will be able to charge off and deduct as a loss either that 50% of the original amount they're going to charge you, as well as getting 50% from collections, or 100% if they're... 'creative'. This can often reduce incentive to negotiate.