Recent initiatives that overstate health insurance coverage for well-being conflict with the recognized antagonistic facts identified by the determinants of health that identify health care as an intermediate factor. By using a network of controlled interdependences among multiple social resources including health insurance, which we reconstructed from survey data of the U.S. and Bayesian networks structure learning algorithms, we examined why health insurance through coverage, which in most countries is the access gate to health care, is just an intermediate factor of well-being. We used social network analysis methods to explore the complex relationships involved at general, specific and particular levels of the model. All levels provide evidence that the intermediate role of health insurance relies in a strong relationship to income and reproduces its unfair distribution. Some signals about the most efficient type of health coverage emerged in our analyses.