This is false, and I am 100% confident in that assessment. Insurance companies are not the main drivers of high health care costs. They are barely drivers at all. I mean, just look at the claims here:
1. For profit insurers deny claims too often and people die as a result;
2. For profit insurers are causing medical care to be too expensive.
These are contradictory statements. The only way that both can be true is for the effects to be quite small. And indeed, for-profit insurance's effects on overall costs is small. Administrative costs traceable to for-profit insurance adds maybe 5-7% of overall cost, at most (and that's before accounting for any savings generated).
A much more important source of administrative costs comes from the problems of a) the ridiculous inefficiency and non-interoperable EMR systems and b) procedure coding. So much money is spent in implementing EMRs that suck, so then they have to be replaced, and some companies build their own, which still suck, and nobody can talk to each other. And then physician practices spend a lot of time upcoding procedures to maximize reimbursements, and then the insurers want to fight against upcoding, so we get appeals processes, etc.
Neither of those categories of costs is traceable to for-profit insurance. I won't say that for-profit insurance doesn't in some cases aggravate them -- I wouldn't really know either way. But upcoding is a direct result of how Medicare reimbursements work, and I do not think a private insurance system would continue to use this technique if the entire field wasn't built around it. And I don't even know what to say about EMRs, the suckiness of which is almost incomprehensible to me, except that it seems to be a provider thing, and in particular large providers like hospitals.