That's a good point. And, it's easy to get access to the dishes with a drone. They're either on top of the station or merely behind a fence (we had both). You would need some insider information, though, or to spend a lot of time observing and experimenting. Most stations have multiple dishes and at any given time the station may be playing recordings from tape rather than showing satellite feeds directly. At the station I worked at, we rolled morning kids shows, prime time network shows, Rockets games, and later some news segments, from satellite directly. Everything else, about 85% of our programming, came from tape. That's probably evolved since then.
I wonder how much of satellite transmissions have gone digital (and thus, likely to be something you could only jam and not replace) in the ~20 years since I was working in the industry. It wasn't even really on the radar when I left the business; even stuff that had a major digital component, like automated advertising feeds, were still being transmitted analog for the video and just the metadata was digital and sent via another mechanism (internet, I think).