Square brackets are mainly used to enclose additional information that was not actually said by the speaker. For example, if somebody says
He shouldn't be allowed to get away with this
A reporter might decide that it is not clear who He refers to, and add the name in square brackets:
He [John Doe] shouldn't be allowed to get away with this
It could be used to correct grammatical errors in the original speaker's text, as in your first example, But your second example certainly isn't a valid use of square brackets, because the contents of the brackets is fundamental to the sentence, not additional information.