Contrary to the song, he wasn’t born on a mountaintop in Tennessee — he was actually born in a part of western North Carolina that later became Tennessee. No matter, his legend was big enough for several states to claim a part of.

And he didn’t kill himself “a b’ar when he was only 3” — though he insisted that at age 39, armed with only a knife, he killed a fully-grown black bear.

In Michael Wallis’ splendid biography, “David Crockett: Lion of the West,” nearly every story or legend told about America’s most famous frontiersman is proved to be an exaggeration — but, happily, nearly every tale about Crockett (a great many originating with Crockett himself) has a hard kernel of truth at its core.

David Crockett — he preferred his formal name and never signed “Davey” or “Davy” to a letter — “believed in the wind and in stars. This son of Tennessee could read the sun, the shadows and the wild clouds full of thunder. ... He traversed the land when it was lush in the warm times and when it was covered with the frost that Cherokees described as ‘clouds frozen on the trees.’ ”

He was born in 1786, one of nine children to a hardscrabble family of Scotch Irish stock from Ulster. (“They became,” writes Wallis, “the first settlers to call themselves Americans.”) Debt hounded the Crocketts all of their lives, and David never entirely escaped it. As a young man, he achieved a sizable reputation as a marksman and supported his family with game as a hunter. He distinguished himself while fighting with Andrew Jackson in the Creek War — actually, “the tragic Creek War ... which was in reality a Creek civil war between opposing factions of the tribe.”

Although he only had a few months of formal education, he read Shakespeare and Ovid and was elected to Congress in 1826. His legislative record is dubious, and he seems to have used most of his time in Washington composing fanciful autobiographies. His record for integrity survives historical scrutiny, though he was not above using sly political tricks. He was one of the first politicians “to perfect the tactic of ‘branding opponents as being too elite.’ ”

As a populist, though, David Crockett was the real thing: “without fail, Crockett always took up for the settlers; he believed they suffered at the hands of land speculators.” And, following his own motto, “Be always sure you’re right — then go ahead,” he was on the right side of one of the most important American issues, voting against Andrew Jackson’s Indian Removal Bill. A vote, he said, that “will not make me ashamed in the day of judgment.”

Too honest to be a successful politician, Crockett burned his political bridges behind him, and after a defeat in the 1836 congressional race, told his former constituents, “You may all go to hell, and I will go to Texas.” Much to his wife’s chagrin, he left his home and family to reverse his fortunes in the nascent republic. Texas, after all, “promised Crockett a fresh start and new opportunities for homesteading as well as politicking.”

Unlike his superprojections played by Fess Parker and John Wayne, Crockett did not go to Texas to fight for liberty. He “had never heard of the Alamo and certainly had no thought in taking part in any revolt against Mexico.”

Nonetheless, he chose to stay and fight with Jim Bowie and Col. William Travis and the badly outnumbered defenders of the old Mexican mission/fort.

In doing so, writes Wallis in one of the memorable flourishes that makes his biography so readable, he and the men who died with him “transformed the Alamo into an American cultural icon.” As Wallis puts it, “one may say that, figuratively, Crockett invented Texas.”

In the end, Crockett deserved the status of America’s first real folk hero — he actually lived to see himself portrayed on stage as Col. Nimrod Wildfire. “The curtain calls ... have never ceased for the Davey Crockett of imagination.”

Nonfiction

David Crockett: The Lion of the West

By Michael Wallis

W.W. Norton; 320 pages; $26.95