Is murder unconstitutional?

In her opening statement at tonight's Democratic debate, Hillary Clinton stated:

I want to stop the health insurance companies from discriminating against people because they're sick. You know, it's unconstitutional to discriminate on the basis of race or gender or ethnic origin or religion, but it's okay to discriminate against sick people and we're gonna end that, because it's time we said, "no more."

[Applause]

So, is it reasonable to ask which part of the Constitution forbids private parties, like insurance companies, from discriminating "on the basis of race or gender or ethnic origin or religion?" And, if that section doesn not turn up, is it reasonable to question whether Hillary Clinton has a firm command of the basics of our founding document? Or maybe it was a simple slip-up. Maybe Hillary Clinton does not equate laws with the Constitution. Perhaps there is some other explanation. It would be nice to know the answer. [Disclaimer: if the U.S. Constitution is merely an antiquated document preserving historically interesting but outdated ideas, please disregard these questions.]