I see your point, but I'd posit that the second aspect is the opposite of how moral hazard is normally taught and explained, which is a ratcheting up of risk due when one is insured, rather than an overuse of some public good, which is normally thought of as a tragedy of the commons: I have access to a public good, I may as well milk it for all its worth. Tragedy of the commons does not affect how somebody treats their own body.

At a higher level though, you need to look at what is actually driving healthcare costs. Is it the (relatively) inexpensive but overused checkup/preventative costs, or is it the expensive and overused prolonged treatments for preventable/chronic diseases such as type-2 diabetes, lung cancer, heart-attack/stroke, etc.

Eighty-six percent of all health care spending in 2010 was for people with one or more chronic medical conditions.

http://www.cdc.gov/chronicdisease/overview/index.htm