Yes, exactly. She had just watched them have a parent/child interaction that was apparently a continuation of something earlier, and while there was argument, there was no contention about those roles. Harry didn't question his father's authority -- in fact, he eventually apologizes, apparently for not behaving as he had promised -- and Severus didn't turn to Dumbledore and try to make this a school issue, although he probably could have after what Fred said. This is where Mrs. Weasly believes that this isn't Severus maneuvering for status (after having maneuvered for sex).

Bill is likewise thinking "oh no -- one of those conversations! Well, doesn't look like it's the first time...."