It will not do to change every that to a which—a corrective feat one instructor reported with an air of accomplishment.
Plain Style, p. 109
A grammatical rule should ultimately help you write better. It serves this purpose if it anticipates a misunderstanding between you and your reader, not just an objection from your copy editor. If it does not help you to avoid real misunderstandings, the rule is just a "shibboleth", i.e., an aspect of usage that identifies social position of the language user. This is Jonathan's objection (in his comment to last week's video) to the that/which distinction, and I'm going to see if I can counter it this morning.
I should begin by saying I feel the force of his objection quite keenly. I didn't know how to distinguish between that and which until I became a copy-editor myself. And I think if there is talk of a shibboleth here, it is mainly one that identifies the language user as a copy-editor. As Jonathan notes, perfectly articulate users of both American and British English don't make the distinction that the Chicago Manual of Style makes a mark of "polished American prose".
Moreover, there are the pseudo-editors and grammar snobs who insist on the that/which distinction in plainly stupid ways, like the instructor Lasch says changed "every that to a which". No, you must know when to use that and when to use which. And my argument for observing the difference is precisely that it forces you to decide whether you are deploying a restrictive clause or not.
A telling example of the need for such decisions can be found in the work of Karl Weick, a top-rated organization theorist who is actually renowned for his style:
A book that is about interpretation would be a sham if it were grounded in paraphrase that rubbed the nuance off an author’s remarks, discouraged reader exegesis, and squelched divergent readings. (Sensemaking in Organizations, p. xii)
I have suspected this sentence of being strategically (i.e., intentionally) ambiguous for some time. Weick is here justifying his use of extensive quotations throughout the book, which are often inserted into the text without comment, i.e., without Weick's own interpretation (though this is not something he is explicitly trying to justify). He is presenting this not only as a virtue, but the alternative as a vice (a "sham").
But notice that the dangers of rubbing off nuance, discouraging exegesis, and squelching readings are only arguments against paraphrase if they are used in a non-restrictive clause to modify the noun "paraphrase". Otherwise they are just arguments against paraphrasing badly, which goes without saying. That is, only if these dangers are inherent in the art of paraphrase, not descriptions of particularily defective kinds of paraphrase, can they be used to claim that "a book grounded in paraphrase is a sham". Using Chicago's rule, we would write:
A book that is about interpretation would be a sham if it were grounded in paraphrase, which rubs the nuance off an author’s remarks, discourages reader exegesis, and squelches divergent readings.
But that is of course false. Everyone who interprets texts for a living knows that there are perfectly good ways of paraphrasing, i.e., paraphrases that do not, for example, discourage exegesis but, rather, encourage readers to find the source and read it themselves.
So Weick might mean that when he paraphrases he does it so poorly that the result would be an interpretative sham. No, of course not; he can't mean that. Which is why I suspect he is trying to have it both ways here. But if he had committed himself to the that/which rule, he would have had to decide how he wanted to modify "paraphrase". He would then have had to rethink the claim he is making. And this, I would submit, is a good reason to have a clearly marked occasion to reflect upon restrictive and non-restritive clauses. Poor usage here may be a shibboleth of muddy thinking.