The problem is more so that SP will be making money off the copyright, so most large companies with copyright will look to protect them.
yes but that isn't exactly how it works. If I own a manufacturing plant I can make whatever I want doesn't matter if there is a copyright it's selling it that would get me in trouble. In terms of custom keycaps we are talking about contracted work and in manufacturing to contract the manufacture has less liability because the contractor is the one using the image. It's not the same as say SP coming up with a bunch of keycaps with car manufacture emblems or game logos or whatnot. Usually when a company says they can't make something because of copyright it's because the company owning the copyright has in the past sued somebody or sent a cease and desist letter at some point. Think about all the caps that have been made though group buys that shouldn't have been made if the manufacture used copyrighting as a reason to not to. If you look at it from a purely technical standpoint every keycap would need a copyright release because of implied copyright from the person that designed it. Even if all they did was chose the color and font they still created it so it is their sole intellectual property which falls under implied copyright.
And to be honest from a legal standpoint group buy keycaps are such a small scale it wouldn't even be worth pursuing and I doubt any company would care except for coke and disney. they go after everyone for anything. Usually when a company says they can't make something because of copyright it's because the company owning the copyright has in the past sued somebody or sent a cease and desist letter at some point.
Not with keycaps but with other faux branded items I have experience in this. I've gotten one time copyright releases from all sorts of companies from BMW to Ski (soda brand). Usually a simple phone call and explanation is all you need when a manufacture need a copyright release. But it's never hard to find a place who doesn't care anyway. From what I have found many places see it as free advertising.
Never hurts though if you run into trouble just call the company and ask worst you get is a NO.