Neither speaker makes this claim. The discussion is only about a rule that bans students from citing certain non-peer-reviewed sources. Neither the student nor the professor talks about the role of peer reviewed sources, or what sources are required.

The student agrees with this but the professor disagrees. This is the point of disagreement. The student claims that a citation ban conflicts with the freedom to read any sources one desires, thus equating the two. The professor differentiates between citation and reading.

Neither speaker makes this claim. Only the student mentions censorship at all, and even then, only to say that limitations on what sources students can read would be censorship. No one talks about what might justify censorship.

The professor might disagree with this (although “reliable support” and “solid support” aren’t necessarily the same thing) but the student never talks about the quality of non-peer-reviewed sources or their ability to support claims.

The student makes this claim, but the professor doesn’t disagree. The professor’s argument doesn’t touch on whether students should have this freedom or not, just that the citation ban doesn’t conflict with this principle.