A bag of word-vectors has no sense of order. We fix that by adding a position vector to each word. Flip the order and watch the input matrix actually change.
The position rows never move — slot 0, slot 1, slot 2 are fixed. So swapping the words changes the sum. Strip the position part away and both sentences would be the same set of rows, and “dog bites man” would be indistinguishable from “man bites dog”.