Firstly, I'm sure she does coke. If not, she's reeeeaaally missing out on something.
Secondly, she's not doing coke in this video. It's obvious. Also, Taylor is pretty intelligent and professional, and I think she would be the last person on earth to be caught doing drugs.
It would appear that Viacom invoked the Digital Millennium Copyright Act to suppress an image of Taylor Swift engaging in an authentically human act.
A typical case of making something worse by being overprotective (they should have better let her just blow her nose normally like a human being (without literally deploying a trained "snot squad" consisting of half a dozen active duty personnel