Well, yes and no.

Providers are (I believe) required to let you bring your own equipment. Every DSL or cable service I've seen has allowed this.

However, it is also required that the modem you plug into the network accepts and runs firmware provided solely by the network operator. They can update your device at any time and there's nothing you can do about it.

So yeah, you can run your own hardware if you want, but the ISP will run their software on it whether you like it or not.