Private Insurance Companies claim that they can't compete with Medicare.

Maybe they mean they just don't want to.
"private insurers have told the Bush administration that they will not expand their role in Medicare if they have to serve large multistate regions, ...Large regions will force health plans to serve rural areas that they have historically shunned, administration officials say. "

I think they mean "would force health plans to serve rural areas if, for some strange reason, they were to decide to stop shunning them." Personally I am willing to believe the insurance companies that they can't serve large regions without losing money. This in spite of the fact that the Bush plan would pay them more per patient than medicare costs. It is well known that the assumption that the public sectro is always less efficient than the private sector does not correspond to this case.

It is also possible that Bush was not generous enough to satisfy them and that they want to be paid extra and allowed to cherry pick densly populated regions.

Now what will happen ? My guess is that Bush will flip flop again and abandon the large regions and claim the issue is unimportant.