The "samurai" were hardly an effective power by 1876 (not to mention that the shogunate had long been out of power by that point - the film would've been more believable if it took place in 1863, but that wouldn't have been nearly as sexy as there would've been guns and warships, etc. and Cruise wouldn't be post-Civil War, he would be in it). There hadn't been nearly any internal military conflicts in Japan in almost 250 years at that point, the samurai weren't nearly as well trained as they were during the height of the power. If anything they were largely discontent - marginalized by a class system that kept them under a strict code of conduct while preventing them from reaping the rewards of commerce. There's a reason the Meiji restoration happened in 1868 and a reason why there was large discontent in Japan during the late-Tokugawa era - the government's power was crumbling, it wasn't nearly as effective as it use to be.
While I can believe the premise of a rogue samurai village fighting to "keep the old ways" - fighting for a return of the shogunate is almost laughable.
It did please me though that they were showing Tom Cruise woodblock prints to "educate him about the ways of the samurai." Kind of hard to tell but it looked like they were some of Yoshitoshi's more gruesome prints - for example from his series '28 Famous Murders with Verse': http://www.yoshitoshi.net/series/murders.html Thankfully at least that's a series that was printed before 1876 so at least that's marginally correct - huzzah!