The real observation is well documented. In 1953 a juvenile female named Imo began carrying sand-covered sweet potatoes to water before eating them. The habit spread slowly, first to her playmates and mother, then outward, following lines of kinship and age. Adult males, the most peripheral animals socially, were the last and least likely to adopt it. Uptake took years, not days.
The embellishment arrived in a 1979 popular book, which asserted that once some threshold near one hundred animals was reached the behaviour appeared spontaneously in troops on other islands. The primary reports contain no such threshold and no such island jump.
A 1985 analysis by the philosopher Ron Amundson traced the claim back through its sources and found the numbers had been supplied by the retellings rather than the research. The genuine result, gradual social transmission along social ties, is the more useful one.