One correction, though: it claims that the distinction between that and who is tested on the SAT and ACT. That is untrue. Errors where which is used for people do sometimes appear (e.g., "the politician which resigned from office"), but these tests do not assume that Mark Twain was ignorant when he titled a short story "The Man That Corrupted Hadleyburg." They actually sidestep the issue altogether. In other words, they would never give you a sentence with that underlined and referring to a person.
I presume that the author of the piece got that misinformation from some test-prep book or other. Often, the authors of those books really haven't systematically studied what grammatical points do or do not appear on the tests. They just copy usage peeves from other books.
The second rule that the author claims is an SAT/ACT rule (never use "they" for a singular antecedent) is one that is enforced by the test-makers. In this case, while I agree that using "they" for singular antecedents of indeterminate gender makes perfect sense (and has a long history among reputable writers), as a practical matter, the overwhelming majority of English teachers and copy editors disagree. There's much more unanimity on this point than there is on the who/that distinction. So while I will champion your right to use singular "they" in your writing, you should be aware that it may hurt your grades if you use it in a school paper or if you fail to correct it on the SAT.