I have DirecTivo. It pulls its guide data off the same satellite feed it uses to get the programming itself. It only calls home for PPV purchases and monthly data collection. Mine, however, have not called home in like two years.
I do pay for the service, but my Tivos have a lot of added value that did not come with the basic service offered by DirecTV.
He's right about the Tivo forums, BTW. You're going to have to read read read and then ask a specific question in order to get any help there.
Tivos CAN use broadband, one of mine has a 100baseT nic in it that I put there myself. It used to be controllable via the web using a webserver it serves itself that hooks into the Tivo app, but I took that down because it was using up too much of the Tivo's limited RAM.