I personally really love the Kirk Douglas movie Lonely Are the Brave. I was surprised to see this quote on it's Wikipedia page (emphasis mine):
President John F. Kennedy watched the movie in the White House in November 1962. In his memoir Conversations with Kennedy, Ben Bradlee wrote, "Jackie read off the list of what was available, and the President selected the one [film] we had all unanimously voted against, a brutal, sadistic little Western called Lonely Are the Brave."
I haven't seen the movie for years, but based on my recollection I don't understand why this movie would be considered "brutal" and "sadistic." Were people reacting to the horse being shot at the end, or something else? This seems especially strange since most Westerns generally involved killing scores of Native Americans and/or big shootouts. Some of those elements were present (shootouts) in Lonely Are the Brave, but they were greatly subdued in comparison.
The basic plot line as I recall was Douglas goes to visit a friend. He finds out that her husband is in jail for giving aid to illegal Mexican immigrants. Douglas gets himself thrown into jail on purpose so he can break his friend's husband out of jail. Douglas breaks out of jail, and rides off into the hills on his horse. Law enforcement proceeds to chase after Douglas. Douglas is on the verge of getting away when he and his horse are injured. The horse is shot and Douglas goes to the hospital. Douglas's character throughout is a portrayed as a tough, strong willed individual, not one that treats others brutally out of sadistic glee. Douglas himself seems to agree since he described his character in Lonely Are the Brave as pure and good.
Another factor could be that Kirk Douglas in his own words tended to play villains, so maybe people were reacting to him as the lead and making assumptions. However that doesn't seem to fit either if the person being quoted above (I assume this is Jackie Kennedy) saw the movie and is remembering it as "brutal" and "sadistic."