When asking whether hospitals engage in cost-shifting--subsidizing inadequate public reimbursement with private insurer fees--the question is partly one of framing. One way to look at it is that the private insurers pick up the slack for the public programs. Another way to look at it is that once private insurers have covered the hospitals' fixed costs for physical plant, and so forth, as long as the government programs cover a little more than the marginal cost of serving the patients, they're actually slightly subsidizing the private patients. It all depends on whether you assume that people in the government programs would have consumed (and paid for) any healthcare absent the public programs. In the case of Medicaid, maybe not, but in the case of seniorcare programs, that's probably at best only partly true.
Another question you need to answer, as I noted yesterday, is how much negotiating power hospitals actually have with private insurers. I'm not sure there's a good answer for that question, but here's a look at what happens when negotiations go nuclear.