In some states, notably New York, TWC and others are required by law to open up their networks to competing vendors at a reasonable price. That is why Rochester, NY even has Earthlink as a provider on Time Warner's network.
Verizon is non that market because Frontier is the incumbent phone company and it would be very difficult to wrest market share from them (though Time Warner's done a pretty good job with Digital Phone). There is no law preventing Verizon from entering the Rochester market; it's simply not feasible for them to do so.
While states and local governments may not have much power, the customer always does. TV and Internet are not (generally) essential to live for a residential customer. Rochester, NY and other proved that today when Time Warner backed off their plans to expand their consumption-based "test" in four new markets. They haven't given up, but the customer backlash -- not the government alone -- was enough to tip the scales.