Not only is it arguable, it is the correct argument. I would say that the reputation is probably more prevalent in pop history books and in stupid nationalist arguments online than in contemporary historical scholarship. There are a solid number of good posts on this subreddit on the topic of the longbow's battlefield effectiveness. /u/valkine wrote this comment just the other day that covers some of the historiography behind the debate. I wrote this answer a while back that focuses more on the tactical effects of longbow archery in the Hundred Years War. As with practically all weapon or military technologies, any conversation that places too much emphasis on technological determinism is going to be mostly nonsense.