That’s absolutely ridiculous. I mean, fine, the school gave her knowledge, but it gave everyone there knowledge. It wasn’t like they set out to give her extra special “here’s how to drain magic from our world” lessons they weren’t teaching the other students. They gave everyone the same information, and her being the only one to use it the way she did is entirely dependent on what kind of individual she was, not the place she acquired it.
That’s actually one of the things that makes Neighsay even more wrong. What he seemed to be thinking along the lines of was “hey, what if this knowledge being taught to other races led to other countries/creatures using it as a way to one-up Equestria and destroy it/conquer it,” as opposed to… a psychopath using it in a demented crusade for power. Cozy Glow doesn’t even have an actual agenda beyond the pursuit of power, which is probably part of why he seemed rather dumbfounded and scared when he asked her “why are you doing this,” followed by her explaining
(and no, Tirek’s knowledge just isn’t a part of the curriculum; someone with that sort of information is honestly kinda too dangerous to be left alive if evil, come to think of it, that goes for both of them)
Oh, and let’s not forget that them “disregarding someone who pointed out that the lessons learned there could be used against Equestria” was entirely about non ponies learning the lessons. Had Twilight’s school been entirely pony based, Neighsay likely wouldn’t have even considered the possibility. A fact amply demonstrated by the fact that Flim and Flam’s “school” passed with flying colors, despite by their own admission having just copied every other page of Twilight’s guide.
Which yes, they did. You can’t give Neighsay full credit when having what might generously be considered a valid point is undermined that he’d only selectively have it, against non-ponies.
Also, trusting Flim and Flam, giving them his blessing when one of his complaints was that the teachers were unqualified.