Nobody's running the F1 race from tape...
I'd be curious to know if there's much digital and/or crypto in those signals too - part of me suspect the satellites themselves are mostly "too old" to be doing anything except analog - although I do sometimes notice the resolution on MotoGP races drop significantly, I think that's last mile cable bandwidth problems when the Sunday night movie starts pumping full HD into all my neighbours houses, rather than the signal from space...
Most satilites operate as a really dumb "bent pipe".
You transmit a signal on one frequency, and it amplifies and re-transmits that signal exact same signal on another frequency.
There is no decoding and re-encoding of the signal. The satilites is completely agnostic to the formatting, and encoding of the signal. All you need to do is replace the equipment at each ground station and you can transmit encrypted digital.
On the flipside, I don't think satilites do any authentication of the signal they are retransmitting. If someone transmits a stronger signal, the satilites will lock onto that and retransmit that instead.
However, the receiving equipment probably does authenticate and won't accept the hijacked signal, so all you get is a jamming effect. But the satilite itself is hijackable.
Here's an anecdote about one sport in particular - UK horse racing. There's a pay TV channel (Racing UK) that broadcasts races live. They would bring their broadcasting equipment to each track, and upload the live raw video over a satellite link. This stream was then downloaded at their head office, where it was mixed and graphics were added, before it was re-uploaded to (another? the same?) satellite as the 'official' TV channel.
With the right equipment, you could view the raw video feeds yourself, rather than watch the re-transmitted official channel. This gave just over a second or so of improved latency, which, for some serious in-running gamblers, was a crucial advantage. But about five years ago, Racing UK started encrypting their live feeds. Nowadays, only a few people with insider information can obtain the 'faster' video...