I mean often times they just have a script that looks for the trademarked terms (or in some cases, visual matches, or music for video), so it does matter using such things. At least when something it released, if it's largely original work using trademarked names/logos is an easy way to shoot yourself in the foot (and can result in very early detection).
I also doubt takedowns are usually a higher-up hearing about said projects and "ordering the strike" (probably just that it popped up on an automated/intern-ran script), that's why I think even the easiest changes would be good to do. Because they probably aren't ever going to see Jimmy Eagle even if it were uploaded and popular.
The video part isn't really important to my point, just the general idea that involving trademarked stuff is basically a multiplier for risk. Some simple changes and fans will still see what it is and like it, scripts won't. And people fail to see this too often, so I don't think people should encourage it because "it's probably fine".