There has been so much crap written about that period in our history, it's sometimes hard to sort through it. From the stuff written at the time(violence sold newspapers then, too) to current movies and historical writings, you have to dig through it to try to get to facts.
For a time- I think it's still going on with some academics- the 'new' understanding was that guns were far less common than had been thought, etc. Kind of an early version of Bellesiles. And of course we got the 'Good Native Americans-Bad Whites' stuff. As to the latter, it wasn't nearly that simple. Were the Indians screwed over? Yes, far too often. Were they paragons of virtue deserving worship? Hell no. From problems in the East clear up through the end, it was far more complicated than it is usually depicted. There were forces working that made it very simple in one way; lots of people in other parts of the world looking for a place that would give them a chance for a decent life, a better life, and they needed places to live. Eric Flint just brought out a new book, The Rivers of War, that covers some of this real well in the War of 1812 period. In his alternate history, the Cherokee are being convinced by some to move west voluntarily, as a united people who can make a nation there, instead of being forced out of their current lands as refugees in a few years. No, it's not fair, and the Cherokee and some other tribes deserved much better treatment. But to borrow a line, "Deserve's got nothin' to do with it". He does a very good job of outlining things as they really did sit.
As to violence and guns, a lot less violence than was painted(both for romantic outlook and by people who wanted to show how nasty things are when people have guns). As Louis L'amour put it, when the butcher, the baker and the blacksmith either fought in the Civil War or had dealt with bandits and Indian attacks, or both, trying to take over the town pretty much guaranteed a short life and a dramatic death. But the violence was there; pretty much guaranteed given the times and conditions. And again, so much has been written about it by people with a political and/or social point to push, it's hard to get through to the truth of it.
As to the movie scene of two men walking down the street toward each other 'till they draw, I don't think I've read of a witnessed account. Strictly speaking, that doesn't mean much; a lot of things happened that didn't leave written accounts by others. Other types of shootings, definately did happen. I don't have the piece anymore, but L'amour once wrote of going through newspaper morgues in cities and small towns across the west. He only counted cases where there were witnesses as to how they happened, and came up with more than 200 as I recall, including fast-draw incidents.
Side note: something that ticked me off with Tom Clancy was a passage in The Bear and the Dragon where a FBI agent was telling a Russian about how little crime there really was in the old west(true), and that fast draw and hip-shooting doesn't work(bullshit); with all the research he did, you'd think he'd have had that right.
It was a really interesting time in history, where you could find illiterate miners and the sons of European nobility drinking side by side in a saloon, fortunes were made and lost, legends created, and customs that affected the world born and/or solidified. It was far too interesting and important to be screwed around with by politically-motivated idiots with multiple degrees and/or a modern politically correct point of view to force on people.