It has been more than a week since Rick Santorum went on the Sunday talk circuit and made news by saying that John F. Kennedy’s famous 1960 speech about his religion made him want to “throw up.” But the comment still reverberates on the campaign trail, including places like Ohio, where he and Mitt Romney have battled for the blue-collar vote, and where lots of people go to church and remember JFK.

Santorum got some bad headlines for the incident and it wasn’t long before he was backtracking on his comment. But it was his word choice, the vomit allusion, he regretted—not the substance of his remarks. And the press could have done a better job explaining that substance and its problems.

What apparently disgusted the senator was the notion that separation of church and state in America should be absolute, an assertion he attributed to Kennedy:

To say that people of faith have no role in the public square? You bet that makes you throw up. What kind of country do we live that says only people of non-faith can come into the public square and make their case? That makes me throw up.

Journalists are accustomed to having to work hard, sometimes, to translate Santorum (as my colleague Greg Marx explored recently), but there were clear problems with his JFK statements that should have taken reporters beyond headlines like “Santorum: JFK speech ‘makes me want to throw up,’” or merely asking, as George Stephanopoulos did, “You think you wanted to throw up?”

Most initial reports did not. While some stories the next day made reference to Kennedy’s speech—a few of them quoted it—in the context that it had made Santorum want to vomit, the stories did little more than that.

For example, many reports failed to mention that Santorum’s version of what Kennedy said was wrong.

Kennedy was, of course, a man of faith in the public square, a Catholic at a time when many protestants could not imagine one as president. That is why he made his speech. And he never said anything like what Santorum attributes to him, that only people of non-faith were welcome in the public square.

Santorum’s claims on Meet the Press were also open to scrutiny for how he characterized the views of the founding fathers:

The original line that you didn’t play that got—that President Kennedy said is, “I believe in an America where the separation of church and state is absolute.” That is not the founders’ vision, that is not the America that, that made the greatest country in the history of the world.

But, as George Packer noted, a clear separation of church and state is a lot like what the nation’s founders had in mind:

Kennedy had nothing to say against believers entering public life, or believers bringing their religious conscience to bear on public policy. He spoke against any move to make religion official. The Constitution speaks against this, too—Article VI establishes an oath to the Constitution as the basis for public office, and explicitly prohibits a religious test, while the First Amendment forbids the official establishment of religion and protects its free practice.

In fact, Jefferson famously spoke of “a wall of separation between church and state.” And here’s James Madison, arguing that the division between religion and government is good for religion: “The devotion of the people has been manifestly increased by the total separation of the church from the state.”

This sort of fact-checking and analysis did come in posts at outlets like Salon and Slate, but aside from an op-ed in The Washington Post, coverage by the mainstream media was one-dimensional—the vomit comment—and missed an opportunity to contextualize and explain the debate over church and state separation.

Erika Fry is a former assistant editor at CJR.