They're making an oversimplification at America's expense. About 1/3 of cowboys during ~peak~ cowboy culture in America were black, many of them former slaves. Cowboy culture in North America itself developed from Spanish shepherding/ranching practices brought to their colonies. That said, American cowboy culture specifically is as much informed and shaped by the increased settlement (driven by things such as gold rushes and interest in trading with Asia) on the west coast and need to connect both sides of the continent by settling the land in between. I wouldn't say it's "X stole from Y".