why couldn't it? Unless the remote system (where the video is being received) is untrustworthy. In my scenario I was describing network traffic encryption, for a theoretical where the entire network between the video-sending and video-receiving linux systems could be 'hostile', but not encryption of the video itself, I was assuming that the location where the video is being sent to is trustworthy.
If the video needs to go to a remote storage location where you want files to be written to disk, but nobody else to be able to read them, that's a somewhat more rare problem to solve. Possibly something involving a virtual machine with a dm-crypt/LUKS implementation for FDE.