How does using a satellite broadcasting differ from a server on the internet publishing the keys? Both are single points of truth that you'd have to fully trust.

I would guess that a satellite can literally just have a TX radio on this module, so as long as you trust it to have been built and launched securely it can't be tampered with by anyone without space capability?

Whereas a server on the internet could be compromised over the internet.

You could have a server that only sends to the network as well. Just block everything apart from outgoing UDP packets. For the price of development and launch of such a satelite you'd probably be able to afford to make a custom hardware box with hardware random number generator that can physcally only send. In both cases you'd have to fully trust someone to have set up the system correctly. Both wouldn't be something I'd want to rely on.