Wait, there's more!
Bad Company was also a 1972 movie starring Jeff Bridges. It is described as a "thoughtful western" on IMDB. Here is a plot summary from the All Movie Guide:
Set during the Civil War, Bad Company stars Barry Brown as a Northern boy who heads West to avoid getting drafted. He falls under the spell of Jeff Bridges, an easygoing young con artist. Brown joins Bridges' gang of boy bandits, who live by their wits and try to avoid confrontation with adult criminals like David Huddleston. It is Brown who must eventually save Bridges from hanging, even though his intervention may result in his own execution.
Hmm, that 1972 release date is kind of suspicious, isn't it. Alas, there is a connection!
I once heard Paul Rodgers state in an interview1 that the title of the just-released movie provided the 'inspiration' for the name of his newly formed arena rock act. Hence that pseudo-western / tumbleweed-ish sound of the triply redundant title track of the supergroup's first album.
Bad Company
Paramount, 1972
UPC: 97360847642
1 hour, 32 minutes
Directed by Robert Benton
So far we have two completely unrelated movies and two completely unrelated musical groups using this name. What else it out there?
1 Yes, I willingly listened to an interview with Paul Rodgers of Bad Company.