So yeah, it's possible they did.
1. (best version I can find sorry) https://www.reddit.com/r/EnoughMuskSpam/comments/99sbwa/form...
You don't need to be a rocket scientist to see that the sole provider, globally, of a reliable, reusable, orbital launch platform--also a proven heavy and in-development unprecedented super-heavy--is industry leading. SpaceX is at least a generation ahead of not only every other commercial competitor, but also every national space programme the world over.
Usual selling point in marketing of ground based free space optical links is that it is very hard to intercept. Compared to P2P microwave the beam is significantly narrower and alignment requirements higher and the link loss budget is usually tight enough that when the beam becomes visible off-axis due the weather efects (heavy rain or ridiculously thick fog) the link fails.
On the other hand one can extrapolate from results of reverse engineering of the starlink dish. Everything that goes through the space segment is encrypted and entirerity of the high-level control plane is mTLS authenticated, so one would assume that the inter-satellite links work in similar way. Of note is that software in the dish seems to share large swatches of code with what is not only on the starlink satellites but bunch of other SpaceX embedded linux systems.