The confusion over what is taught in Chareidi Yeshivos is semantic.
Lipman and Lapid are talking about high schools (i.e. 9th grade and up) and EY Mom is talking about elementary (i.e. through 8th grade).
I think in terms of the track record of “the Gedolim” it is important to keep in mind that “the Gedolim” is made up of many individuals who often disagree.