Such is actually the case. Or what little is known of it. Glass’s encounter with the bear happened in the wilderness in 1823, which was a long way from any newspapers or traditional ways of telling the story. The historical accounts I was able to find don’t mention the son of Glass, killed by the slimy Fitzgerald (played by Tom Hardy), as shown in the movie version.
This cartoonist’s version of the Glass story, taken from an old pulp magazine (sorry, I don’t know which one), has Glass going after the men who left him to die, but then forgiving them. In the movie he exacts a gory and violent revenge, which makes a lot better cinema, but impugns Glass’s real-life character.
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This article, "A Difficult Man to Kill" from True West magazine, tells what is known of the facts of the story.