Yes, this is the actual issue- assuming a normal distribution in cases that are not normally distributed. People also even leave off the standard deviation, and

Yes, this is the actual issue- assuming a normal distribution in cases that are not normally distributed. People also even leave off the standard deviation, and seem to be mentally thinking of the average as a point rather than considering even the “width” of the normal distribution- so the overemphasis of the average even causes people to misunderstand things that really are normally distributed.