I wonder if there's an Ukrainian service for legal downloading of movies... There are some services for watching them online, but I'm yet to see one for downloading.
But, of course, the author of the sentence could have legally downloaded Sintel or some other free movies. :D
Well, basically it can mean both. It makes sense since downloading and uploading is the same process of moving a file over the network. If you need to distinguish uploading and downloading, you could add more context: «заванта́жив на се́рвер» 'uploaded to server', «заванта́жив з са́йту» 'downloaded from the site'.