The "3 sigmna" rule that you referenced applies to normally-distributed data, and your list of 1 through 100 is not normally distributed. One standard deviation is not defined to be the range that cfovers 68.3% of the data - the actual definition for a standard deviation for discrete data points is:
where and are the data point and the mean, respectively.
This is the formula that Excel's "stdev" function uses. It turns out that if the data is normally distributed then one standard deviation will cover about 68% of the middle values.