Relativity of simultaneity

I believe the conclusions of the moving train thought experiment are incorrect. All explanations I read fail to consider that part of the distance is traveled by the person in the middle of the train. We have these facts:
1) The speed of light is constant
2) The distance (d1 and d2) between each end of the train to the center is the same.
3) The distance d1 (front of the train) will be the distance traveled by the light (dl1) plus the distance traveled by the person (dp1) in the center of the train.
4) The distance d2 (rear of the train) will be the distance traveled by the light (dl2) minus the distance traveled by the person (dp2) in the center of the train.

5) d1 will equal d2, but part of each calculation of d1 and d2 is contributed by the movement of the person. If the person is aware of this movement, he will adjust his calculations for it and will agree with the person on the embankment.