OP describes two separate aspects of moral hazard. You explain the first "I'll smoke all I want because I'm insured" which OP admits is the less important of the two aspects (although I'd bet most people who have even been uninsured for a period of time can relate to the extra fear of going skiing, renting a moped while traveling, or something similar).

The second aspect is what you cite in your footnote and falls in line with the definition of moral hazard, which more accurately is increased risk-taking due to not directly bearing the cost of those risks. In this case the "risks" taken are, for example, check-ups and preventative treatments which may or may not have a benefit justified by the cost.