Thanks for asking such an interesting question!  I've never looked at this one before.

The case of Capital Cities Cable v. Crisp isn't one a lot of people have heard of.  Basically, it goes down like this:

1. The state of Oklahoma wants to discourage drinking and bans alcohol advertisements on TV.
2. Alcohol advertisements are broadcast over cable on transmissions that come from other states that don't have the ban.
3. Oklahoma says that the cable companies must filter out the advertisements before broadcast.
4. Cable companies get mad and sue.

At heart is a constitutional question regarding the 1st, 14th, and 22nd amendments. The cable companies argued that, beyond all other issues, the transmission of cable signals between states is a Federal issue regulated by the Federal government's FCC and that this fact trumps any state law restricting the cable company.

The cable company wins.

The court held the following:

1. While the 21st Amendment does give states the power to regulate the sale and distribution of alcohol, this power does not trump other constitutional rights and is not absolute,
2. The state allowed other forms of alcohol advertising, such as print, and so the cable companies were being unfairly targeted,
3. The state allowed beer commercials to be aired over broadcast networks.

In short, the state could not make a good argument that it was regulating alcohol use in Oklahoma because it was doing so on such a narrow front.  Even were it a broader effort, the Federal government's interest in promoting "diverse cable services" would trump it.