I've heard that too.  Here's what Wikipedia has to offer on the topic:

One of the most common theories of the phrase's origin is that the expression dates from the Second World War, where "nine yards" was the length of an aircraft machine-gun ammunition belt, and to "go the full nine yards" was to use it up entirely. The expression, however, has been reliably dated back only to early 1967, in U.S. Air Force slang recorded in Vietnam.[1] By November 1967 it was recorded in use in the U.S. Army, likewise from Vietnam, and by mid-1969 was appearing in newspaper advertisements in the United States.[2] The first citation in the Oxford English Dictionary is from 1970, in the magazine Word Watching.[3]

Whilst no written occurrences have been found predating 1967, a number of anecdotal recollections suggest the phrase dates back at least a further decade, potentially into the 1940s. One of the better-documented cases is provided by Captain Richard Stratton, who recorded in 2005 that he encountered the phrase during naval flight training in Florida in July 1955 as part of a ribald story about a mythical Scotsman.[4] It has been suggested that there is strong circumstantial evidence it was not in general use in 1961, as Ralph Boston set a world record for the long jump that year at 27 feet, or nine yards, but no news report has been found that made any reference to the term, suggesting that journalists were unaware of it or did not regard it as common enough to use as a pun.[5]

Of course, popular etymology has risen to the challenge; a vast number of explanations have been put forward to explain the purported origins of the term. Suggested sources have been as diverse as the volume of graves or concrete mixers; the length of bridal veils, kilts, burial shrouds, bolts of cloth, or saris; American football; ritual disembowelment; and the structure of certain sailing vessels (where "yard" is short for yardarm). Little documentary evidence has ever surfaced supporting any of these, and many labour under the significant disadvantage of being several centuries earlier than the first recorded use of the term.

Cheers, DW