The main problem I see you running into is that if they decide for any reason to go after you (even just cause now they want your domain), it won't matter if they have a solid legal standing or not. They can afford to tie you up in court indefinitely, and you will likely be unable to outlast them.
Source: This is exactly what happened to my family. We have the same last name as a large corporation, and in the early days of the internet we registered a domain based on a name-related slogan they had used in an older commercial compaign. We were just hosting a basic family website and email, and clearly had no conflicting or overlapping IP. We even checked in advance - they did not own a trademark for the slogan or the name.
A few years later, they decided the wanted the domain for themelves, but instead of offering us a fair price to purchase, they first filed a trademark for the slogan and then sued us for the domain. If we'd had the funds to continue fighting we would have eventually won, but we're just a middle class family and they're a large multi-national corporation with near infinite funds to pay their lawyers. We lost the domain, and it cost us a small fortune in legal fees fighing it.