How does a satellite account get verified?

There's no way the set top box is broadcasting to the satellites. Not that it's technologically impossible but it would add a lot of costs for little benefit to the company. Take a look at the weird LNB used by satellite Internet setups.

I've never had a red button receiver, but my guess is there's an amount of side-band info like weather, news headlines, etc being downloaded alongside the video and the button toggles a display filtered by details from your account information.