Now try sending messages to #iss . That's fun/illegal ;) But if you know Linux and have a high-powered ham station, it's relatively easy if you know what you're doing!
The ISS is perfectly legal with a license, which I have used to contact them.
You also do not need high power at all, you can do it with fairly low power.
Their personal comms would be illegal to interfere with, and take place on private channels yes.
But they have public comms on the station that operate 24/7 that are legal to communicate with and are on HAM radio bands.. Talking to the ISS is something quite a few hams do every time it is overhead.