If a private, but not secret agency has access to the physics and can't engineer it, there's a question of why. As much as we'd like to disassociate engineering from discovery, they're linked together. Engineering leads to further observation leads to discovery and vice versa back the other direction. It's entirely possible there's "new physics" at play even if they're only theoretical to the Discovery Channel right now. Who's to say, really?
So while I'm not gonna disagree with you, and you're right there's a difference between engineering technology and physics itself, I still don't really see the distinction as that important to the discussion here.
Any sufficiently advanced technology is indistinguishable from magic, after all. We're talking about exactly that level of technology, commonly being called physics-defying by many engineers today. That's magic to common understanding, for all intents and purposes, even if it's possible that we could all eventually understand and demystify it given the education to do so.
Until then? Hard to close doors other than just "do we need this for the story". And aliens don't need to be there, hence my whole line of thinking above. That's just another example of "any secret is the exact secret I want it to be" kind of thinking. See also "everything I don't understand is a communist" or more recently, "everything I don't like is woke". I like to make reference to dinosaurs, because no one ever does. Why not? It could be dinosaurs in those crafts too! There's more evidence for that than aliens, right? We know 100% dinosaurs existed, here. They would've had much much more time to develop technology than we did, eons longer. So again why not? "Because it's absurd." Yep. It is. Every argument against it counts against aliens too.