Whether it's illegal or not, Paramount is going to get what's coming to them for punishing true fans who produce what amounts to free advertising.
But even if you had to, it's easily solved: They could have approached him, and said "look, we consider this infringement, and we want to ensure people don't think this is a free for all, but we like it, so why don't you write us a letter asking for permission, and we'll grant you a license as long as you acknowledge that in your twitter feed".
Instead they chose to demonstrate their total lack of understanding of the internet for everyone. It's not like the net is not full of Top Gun torrents to begin with, yet they opt to focus on ruining the marketing opportunity.