I bought my FIL a Surfboard, but that was before I knew his rented modem had a phone jack on it. Turns-out that if he runs his Internet through this Surfboard modem I bought him, the modem rental fee goes to zero. Yeah, he still has the same hardware in his house, and that lets him have the bundled telephone, but as long as he's not running Internet through their modem, it's "free".
So along with one of those inexpensive modems, you buy a coax splitter and a couple of chunks of coax. Then you're out of the modem rental business. Luckily he has his own wifi router (he got that from my BIL), because they try to give you a real fancy modem with everything, but he dodged that bullet. And like you say, with the modem that has built-in wifi, they share your internet with the world, whether you like it or not.