That vs. Which: Is It a Rule?

English can be a tricky language. Take the words that and which, for example. They are both relative pronouns that restate the antecedent to make the sentence clearer, and they both function as either a noun or an adjective in the sentence.

Some say that which is supposed to be used with parenthetical information and that is supposed to be used with information that is vital to the sentence.

For example:
Brianna’s report on insurance benefits, which I sent you last week, should be of some help.
The report that I sent you last week should be of some help.

This “rule” is taught in most English curricula but is it really a rule?