There are multiple plausible ways to do this
And since ElReg doen't go into the details, I think it's fair to give an overview.
The traditional way is to have a second, but considerably stronger uplink. You'd need to be at least about 10 times stronger, which is hard to do. In the olden days of analogue feeds to the uplink, you could even do this to the feed, which is much easier.
Then today many uplinks are fed via the Internet. RTMP can probably be spoofed with some effort.
The most plausible way might be an attack against the Playout Centre. TV-stations today, particularly small satellite ones, don't have people starting tape cassettes or reading continuity announcements any more. Instead it's all just files on disks which are automatically played and put on the air. There are commercial Playout Centres for doing this. Much content will still be shipped to it on tape, but commercials and similar fast changing material is simply uploaded via FTP. Now if you get access to that FTP server, it's trivial to swap out files. If you get the correct length, it'll play seamlessly just as if it was intended that way. If you don't, you might get some hickups.
Getting the FTP password might be done via malware or via an intern at the station.