sensor pattern noise is recognizable to an extent with pros, but usually its paired with highlight rolloff and other similar qualities. For instance, when I watch a movie, I can figure, okay, this was probably one of the arri's rather than a RED, etc. Sometimes, especially with a bit of knowledge on how/where they shot this, you can get an even better idea, close to a specific model. Of course if you're watching an actual movie, this is all after color correction so its more obvious if you have the raw files.

anyway, my point is, people who work with the cameras and files can definitely have at least a good idea of what camera something was shot with, but you'd really need a huge database and computers to do the work to match it exactly. I have colleagues that will show me something they worked on, with cameras they don't own and between the group of us, someone can immediately spot what camera it was shot on. but! like you said, if you post pictures on the internet, and then more pictures/videos with the same camera elsewhere, yeah it should be theoretically possible to match them with sensor noise pattern. they could at least prove its the same model. i'm not sure how much it differentiates between same camera models, but i can recognize my camera models dnp easy peasy. i have not had any caffeine yet so this is likely a jumbled mess of a thought and i apologize.