This graph shows only babies born as a result of spontaneous (non-induced) labor (76% of all participants).
Do babies come on their due dates? Not really. But they seem to come around their due dates. In the survey, only 689 out of 15762 (4.4%) spontaneously arrived on the exact day. But if you look around that date, the numbers get bigger fast... 3864 babies (24.5%) arrived spontaneously between 39 weeks 4 days and 40 weeks 3 days. 7340 (46.6%) arrived spontaneously within a week of their due date. Throwing out inductions makes those percentages even higher: 61.2% of all non-induced babies arrived within a week of their due date.
I also think this graph is important because it shows how meaningless it is to move a due date one or two days. For example I have a chart comparing first time moms to mothers who've had previous births, and it shows about a 1-2 day difference. But based on this graph, who cares about a day?
What I mean is this: a woman who's not induced has a 61.2% chance of giving birth within a week of her due date. Let's say we lie to her and tell her a date that's three days early. Now she has a 60.5% chance of delivering within a week of that "wrong" date. It's not really a huge difference.