The thing that really frosts me about this story is the attitude - professional teachers know best, if fearful parents are going to teach their kids outdated stuff they’d better check with the teacher, most parents are too stupid to teach fourth grade math.
Scary!
If you'll excuse a comment from a professional teacher, I do believe that I know best. It's very simple: I stand in front of a classroom full of kids 180 days a year and observe what works and what doesn't. I'd have to be pretty stupid not to have noticed what helps kids to learn and what leads to confusion. Also, I have several kids at home, and I know what works for them.
I think most parents are smart enough to teach their own kids 4th grade math. It gets a little more challenging when we reach algebra, and rather demanding for most but not all parents around calculus or for different reasons when the kids become teenagers. I also hope that most parents are smart enough that they know they should teach their kids math or at least review the math with their kids daily if possible and at least weekly whether or not that is convenient. I teach the top kids in an excellent and highly ranked school, and perhaps 90% of my students have parents who are involved in their learning. That is what works, and the only administrators/teachers who would object to involved parents are the ones who are not doing their job and hope to hide it.
Teach your kids the "outdated stuff", which is still in our curriculum but not at some other schools. Teach them their math facts, preferably using flash cards, and review annually at the start of each school year. Teach your kids long division. Teach them that the United States is a great country that has done great things (in most areas the schools will more than cover the warts in our history). As a teacher, I can tell you that a combination of some subject matter expert and an involved parent is what actually works best for most of the kids that I see. I'm not in a position to evaluate kids who never set foot in a formal school, since I don't see them, but my students more often than not tell me that they start out at Ivy League schools at or near the top of their class, and I give a big chunk of the credit to their involved parents, along with a substantial share of the credit for the motivated kid and for myself.