That is a tall tale. Hickock’s 38s could barely shoot 75 yards.
This would be a problem - except that Hickock didn’t use a .38.
He, like many others, carried a brace of Colt Model 1851 Navy revolvers. They’re .36 caliber cap and ball revolvers. His were unique in that they were modified to have no triggers. To fire, he simply pulled back the hammers while drawing and released when the weapons were on target; he claimed this was much faster than the standard weapon.
The effective range of the 1851 was greater than what most people could actually shoot with - the ballistic performance of his .36s was somewhere between the .380 ACP and the .38 Special. Effective hits with the .36 have been recorded as far out as 125 yards. The problem was the sight radius of the gun tended to make it difficult to use. That said, Hickock had highly customized guns, probably with improved sights.
Another problem with your idea is that Hickock was observed to hit targets 50-60 yards away as practice on a regular basis. General Custer commented that the man had a supreme mastery of firearms. Hickock often demonstrated his prowess with firearms in public, so many people observed his skills.
See: http://www.bbhc.org/pointsWest/PWArticle.cfm?ArticleID=129
As with many misconceptions with the Old West (and other historical periods), more recent experimentation and research has shown that people really could have been that good.