Darn The Censorious Government

Perhaps somebody can explain this to me. Over at the Volokh Conspiracy, Professor Bernstein rails against censorious public employers, concluding,

Yes, I'm troubled by the fact that the government, acting as employer, has such censorious powers. In the case of the prosecutor, it's pretty much unavoidable. In Mr. Gray's case, it provides another reason to support privatization of peripheral government functions.

Leaving Emerson aside for the moment, isn't that a non sequitur? Does Professor Bernstein really think that private employers are more tolerant of employee speech than public employers?

Returning to Emerson, is running a law school a peripheral government function, or is Prof. Bernstein's concern limited to peripheral functions that don't pay his salary?