I don't know... I would guess that my local cable affiliate knows what I'm watching all the time. I would guess that cable companies can and probably do provide information.
You need to be actively recruited by Nielsen and have meters installed on your TV's to be a part of the sample of persons used to project ratings - either National or Local. Nielsen monitors the viewing habits of a relatively small portion of the nation's households and viewers. They statistically project those numbers out to the total population to report Viewership Ratings, Audience share and other levels of data used by the Broadcasting and Advertising community.
Your Cable provider does have ways of collecting and reporting on viewership (depending on the level of equipment you are using)but that data is not included in the Nielsen ratings you read. Some Cable providers use the data to negotiate rates for airtime but for viewership data to be included in Nielsen reportage, that data needs to adhere to some fairly strict guidelines. To project a National or Local sample "out" to a larger population, the sampled persons need to be in a relative proportion to the characteristics of the larger National or Local group. Cable companies don't do that - they can only report total viewers, Nielsen must be able to estimate viewers of specific demographic breaks such as age, education, Household Income....and believe it or not, dog and cat ownership.
If you are curious, I can answer questions on methodology and such