I don't think this article is saying what you think it says. It's cautioning against cloth masks, like bandanas. It actually affirms that medical masks, those typically used, do work.
I think the point that the parent is making isn't that medical masks (N95) don't work, it's that the cloth masks aren't as effective as people think they are.
It doesn't even say that! There's no no-mask control group to compare against. (And FYI not all medical masks are N95, probably most aren't. It appears that the ones studied there are not N95 but rather the standard disposable surgical masks.)