Don't get me wrong, I'm very sympathetic to this argument. When there's a disconnect between a person's use of a resource and their cost for using the resource, overuse is the likely result. It's the tragedy of the commons all over again.
However, this graph does not by itself prove that the rising cost of health care in the U.S. is caused by insured people running to the doctor every time they get a runny nose. It's probably a significant factor, but I doubt that it's the only one.
Personally, I would like to know more about the relative market power of health care providers and health insurers, by locale. These two kinds of entities are in competition for the money that is paid by workers and employers for health insurance. When an insurer and a provider agree on rates for services, one or the other may bring considerably more clout to the table, and thereby become the price maker, while the other is forced to accept slim margins.
For example, insurers need to be able to tell potential customers that they will be able to go to a nearby facility for treatment. If there is only one health care provider in the local area (which is the case where I live), then the insurer will have to deal with that provider. The insurer doesn't have the option of simply walking from the negotiation table should the health care provider demand high fees for services. The opposite is true in an area where only one insurer operates while there are many health care providers competing for business.
I think it's interesting that in all of the discussion over health care, politicians have successfully demonized the insurance companies with allegations of price gouging (made possible by politicians who have regulated most competition out of the market for insurance), but have made no attempt to similarly attack health care providers for price gouging. I previously linked to graphs like the one below that suggest that health care providers may very well be culpable. I guess voters tend to like their doctors more than they like their insurers.