They both shot Liberty Valance

They spent the whole movie showing you how Jimmy Stewart couldn't shoot a gun. Did you see those scenes or were you texting on your smartphone? Maybe during those scenes is when you posted this comment.

"To me it looked like both Tom and Ranse shot Liberty at almost the same time."

The second version of the shooting, which is from behind Tom, supports that Ranse's shot hit Liberty. The two men are at about a 15 foot distance, and one doesn't have to be a great shot to hit something at that range, even with your off hand.

I slowed the film to frame by frame, and Ranse shoots first. Liberty seems to react to being hit and his own shot goes high, with Tom firing at about the same time as Liberty, but definitely after Ranse has fired and Liberty jerked his hand up to fire harmlessly into the air.

Off this angle, Ranse shoots as he is raising the gun up Liberty's body, with the gun then recoiling higher. It looks to me that the gun is pointing at Liberty when it discharges.

So bottom line--the film backs Ranse having hit Liberty, in my judgment.
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One poster mentioned seeing in the film where the bullet went by a sign hanging down. I watched these scenes over and over again, and don't know at all what he was talking about. Whatever one thinks, there is no evidence where the bullet went. Off the angle, it should have plowed into the saloon wall if it missed Liberty.
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As for the bullet wounds, there would be blood and the folds of the clothes might well obscure the bullet holes, so unless someone checked Liberty, with it probably being necessary to remove the bloody clothes to examine the torso directly, I think it might well be impossible to tell if he was shot once or twice. In the movie, no one checks.
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"When the legend becomes fact, print the legend."

This is the famous quote from this movie. But what exactly are the "facts?"

There were folks all about aware of the shooting--in the saloon behind Liberty, in the cantina behind Ranse, across the street, etc. Notice how men run toward the fallen Liberty from all angles within seconds. It appears that witnesses would number up to a hundred or more.

What did they see or hear?

Everyone single ear or eye witness thought Ranse shot Liberty. No witness mentioned hearing a shot from across the street or noticing a muzzle flash in the darkness. This despite the report of a rifle being distinctive from the report of a handgun. None of the across the street witnesses noticed a rifle shot from their left or right rather than directly to the front. And these were gun savvy frontiersmen used to being around gunshots.

What does this say about history and legend?

In this case the facts back up the legend. If Tom shot Liberty from the shadows, this eluded everyone present.

I think it clear how History would judge this overwhelming eyewitness testimony against the claim of a man who died the town drunk that he actually shot Liberty without anyone noticing.

They both shot at liberty valance. Unless his death was a tremendous coincidence, at least one of the bullets hit Liberty Valance.

And we can calculate that Doniphan's bullet was much more likely to hit and kill Valance. But we can't know for sure.

I thought Tom's story of shooting Valance was to "save the day" and ensure Ranse would accept the nomination and go to DC. THAT was his sacrifice.

The flashback makes me want to echo Annie in "Misery:" "Have you all got amnesia?" and now paraphrasing her: "There weren't two cock-a-doody shots!" Also, in the original scene Tom arrived late, which I took as his real, spontaneous words of the moment.

I think Ranse did shoot Valance - he was close enough to not need much marksmanship.

Seeing it that way makes the story fit together better for me.