The problem, as explained to me by a lawyer (I am not a lawyer, so don't go taking this as legal advice, as I'm paraphrasing what I was told), is that legal departments for really big corporations just care about winning. It doesn't really matter whether they are in the right or not. What's going to make it difficult for you is that they have a huge amount of resources that you don't.
It sounds in your case like they have no actual case for cybersquatting or similar. But that doesn't mean they won't sue you. And if you can't afford to be sued, then that's an automatic win for them.
You also need to evaluate what level of stress and trouble you're prepared to go to to protect the domain. It may suck, but there will be a point at which it would be better for your sanity and your health to let them have the domain and get as much as you can out of them for it.
If I were in your shoes (and I was) I would first visit a lawyer. Get some proper advice.