This is good advice. My 9yr old reads adult fiction, so long as I have read it and don't think there's anything too "adult" in there. I'm saving Heinlein for his teen years lol.
Yeah, a bit of supervision at that age is appropriate, but my advice is don't screen their books for too long! If they're mature enough to be actively seeking out mature titles, you trying to gatekeep them isn't going to prevent them reading what they want to for long. Better to let them make their own choices and discuss sensitive topics with them as adults.