No matter what the legal debate might look like, when it comes down to it playing on a private server is ethically and legally speaking, stealing. It's wrong and shouldn't be done.
However let's view it through the lens of consumerism and capitalism. In this sense Blizzard is on less stable ground.
The goal of Blizzard, or any corporation (yes, even WoW Insider in the end), is to create money for its investors. The way they do this is to create a product that people want to buy and use. They have done a phenomenal job at this. Many of us spend hundreds of dollars a year on World of Warcraft. And if you go to BlizzCon or the World Wide Invitational, you're probably putting thousands of dollars into the economy all over a game – with the lion's share of that money going into Blizzard's pockets.
Ask yourself for a minute what a private server does.
It allows people to play a game they like for free.
What happens when you play a game you like? Especially one that has addictive qualities such as WoW?
You want to play more. And more. And moar!
If you're playing on a private server you'll soon find yourself in a position of wanting to play on the retail servers offered by Blizzard. And what does that mean? Only more money in their pockets.
While the amount of money we're talking about is arguably relatively small compared to the cash-cow that Blizzard is milking right now, no one is denying it's unimportant. But if they can see an increase in profits due to the private server sector, then it's in their best capitalistic interest to allow it to continue since in the end it will create more demand for their product, put more money in their pockets, and make their investors happy.
Some might take issue with the finer points of this argument, and that's okay. There's a lot of holes in my thinking here that can be argued about for years. If you're familiar with the history and philosophy behind parts of the internet, the same justification is often used to support software piracy or warez.
But nonetheless, this does raise an interesting question. Are private severs really all that bad?
I should note that I, nor WoW Insider or anyone else associated with our site, condones private servers or software piracy. It's bad and it steals money from the hard working folks that make these games. Don't do it. Go out and cut some grass or shovel some snow if you need to make money to play the game.