I really don't see where Disney has any legal footing here. Disney gave Starz a license to show the movies on their services. I'm sure there were terms and conditions, but since DISH wasn't a party to that contract, there's no way that Disney can sue DISH under the terms of that contract. If there is any breach of the terms of that contract, Disney would only have an actionable case against Starz. In that case, though, I am willing to bet Disney could only sue Starz if they were complicit and did not try to rectify the situation, which I bet is one reason why Starz is suing DISH.
Now, where it gets interesting is that Starz is suing DISH. No one here knows what the terms of the Starz/DISH contract are, but even if DISH is paying Starz for every subscriber, there could be terms that prevent that. By giving away Starz for free, there is a risk of cheapening the brand. That is the kind of deal that you'd expect Starz to have to sign off on. However, on the other hand, the fact that DISH is advertising it as a special deal and that it's only for a year still maintains Starz's status as a premium channel and encourages people to sign up for DISH, get them hooked on Starz, and then keep paying when the year is up.