"Usually"? My experience with companies large and small has been that if it's a 501(3)c, they're on the "list". For instance, unless you live in western WA, I guarantee the "chances" you'd "recognize" the animal shelter to which we divert our employer match is zero. Now if your chosen charity is "Whitey Uber Alles", meh, maybe it might be an issue. Don't know from experience, who's going to say "no" to an animal shelter?
It boils down to a tax write-off that allows the company to look charitable. But there's a lot of benefit along the way, so who cares of the motivation?