Let me put this up quietly tonight in hopes that everyone is too tired to argue.
There was some nervous tweeting among editors today about the that/which rule. You may have been taught it under various terms: Restrictive (limiting, essential, defining) relative clauses begin with that and are not set off with commas; non-restrictive (non-limiting, non-essential, non-defining, parenthetical) relative clauses begin with which and are set off with commas. You know it is a rule because your English teacher told you so, and besides, there it is in black and white in the Associated Press Stylebook.
There is just one little hitch: IT IS NOT A RULE.
The Fowler brothers suggested in The King's English that it would be a useful distinction to observe; it would tidy up the language a little. But it was a suggestion, not a rule. And later, in Modern English Usage, H.W. Fowler says that since most writers use which for both restrictive and non-restrictive clauses anyhow, the best thing to do is to pay careful attention to the commas. That advice still holds good.
Writing last December in "A Rule Which Will Live in Infamy" at Lingua Franca, Geoffrey Pullum itemized three plain exceptions to the supposed rule:
"The putative ban can’t apply when a preposition precedes the relative pronoun: the town in which she lived is grammatical but *the town in that she lived isn’t.
"The supposed rule should be ignored when modifying demonstrative that, because that which you prefer is clearly preferable to *that that you prefer.
"The rule can’t apply to a conjoined which: We must trust the unknown entity who or which created us is grammatical but *We must trust the unknown entity who or that created us isn’t."