High liability/low probability events cannot be insured using the standard method. Take, for example, the recently renewed terrorism risk insurance program. Private insurers refuse to insure businesses against a terrorist act except at a very high premium.
But just to be clear about how the Price-Anderson Act works, any nuclear accident claims above $12.6 billion (2011 value) would be covered by a congressional mandate to retroactively increase nuclear utility liability or would be covered by the federal government. So there is a chance that Congress would retroactively make nuclear operators pay up rather than pass the costs onto the taxpayer.
Of course, the higher the damages, the higher the probability that the federal government would pick up the cost, but also the lower the probability that such an accident occurs.
In effect, we are taking a risk to reap the benefits of a technology that otherwise would not exist due to the fear of an accident that could occur but is unlikely to occur, at least with good regulation and plant design. I think Vermont Yankee was a good investment in this regard. We reaped the benefits by finding a way to overcome the fear.
Ironically, due to the structure of the liability immunities, as the number of nuclear plants in operation is reduced, the public liability in case of an accident goes up.