Republican presidential candidate Ben Carson waves to the crowd as he arrives to discuss his new book at the National Press Club in Washington, DC. (PAUL J. RICHARDS/AFP/Getty Images)

Dr. Ben Carson, currently running in second for the Republican presidential nomination, told NBC's Chuck Todd on Sunday that he supports a system under which the government would investigate allegations of "extreme bias" on college campuses.

"The way that works," Carson explained, "is you invite the students at the universities to send in their complaints. And then you investigate." He later added, "It's not a violation of the 1st Amendment, because all I'm saying is taxpayer funding should not be used for propaganda. It shouldn't be."

Jeremy Kessler, associate professor of law at Columbia University, agrees that the proposal doesn't necessarily run afoul of the 1st Amendment's protection of free speech. "Public universities are more constrained by the 1st Amendment than private universities" due to their receiving public money, he notes. "Private institutions on the contrary have enormous leeway in regulating speech. The idea that speech in schools would be regulated is not terribly surprising. It goes on all the time."

Carson appears to focus on the former, given his emphasis on "taxpayer funding."

Kessler notes that there's not enough detail to what Carson proposed to evaluate how Department of Education oversight might operate under the Bill of Rights. But he does see one area in which Carson's idea causes conflict: With other Republican groups and activists.

"There are many conservative groups that very opposed to speech codes, because they're seen as politically correct," Kessler points out. "Those sorts of conservatives might find Ben Carson's proposal surprising, because it sounds like it's proposing to fight back against what he perceives as left-wing views on campus by imposing more government regulation." That's the opposite of many libertarian and conservative groups, which seek to eliminate regulation of speech on campuses.

Kessler points out that Carson's proposal appears to mirror the Department of Education's efforts to investigate sexual assaults on college campuses by leveraging Title IX -- an effort that has met with strong objection from members of Carson's own party.

"Using the federal bureaucracy to pursue public policy is kind of a classic progressive idea," Kessler said.

It's very much worth noting the example that Carson used to justify the idea. "I'm sure you heard of the situation," he said to Todd, "where, you know, the professor told everybody, 'Take out a piece of paper and write the name Jesus on it. Put it on the floor and stomp on it.' And one student refused to do that and was disciplined severely."

Carson is referring to an incident in 2013 at Florida Atlantic University. In an intercultural communications class at the school, instructor Deandre Poole asked the class to write the word "Jesus" on a piece of paper and then to step on it. As Poole explained to Inside Higher Ed shortly afterward, it was an exercise he had done in the past. The idea is that students will hesitate, allowing the instructor to talk about "symbols and their meaning."

In that class in 2013, student Ryan Rotela refused to step on the paper, saying (according to Poole) that the exercise was "disrespecting" his religion. After the class, he allegedly told Poole that he wanted to hit him. For that threat, Rotela faced disciplinary action from the school.

Conservatives quickly jumped on the story. Fox News's Todd Starnes wrote a story titled "University Takes Action to Punish Student," implying that the punishment was due to Rotela's not having "stomped" on the sheet of paper. Religious groups marched on campus, and the story spread rapidly, generally in the form offered by Carson. In the face of that outcry, the school apologized for ever introducing the lesson.

Would the Department of Education have found Rotela to be a victim of extreme bias? It's easy to see a scenario in which it wouldn't, presuming instead that a lesson meant to evoke discomfort succeeded all too well.

At the end of that part of his conversation with Todd, Carson explained why he thought this was so important.

"[Y]ou have to be able to look at things from both sides," he said. "You have to be able to evaluate things in a very clear way. And if you're just always looking at things from one point of view, I don't think you're well-educated."