I think your calculation assumes that the waves are traveling parallel to the line connecting Livingston/Hanford. In the diagram below, 's' is the source of the waves.

    H-----L-------s

If instead the waves are traveling perpendicularly to the line between those two cities, they should be detected at the same time.

       s
      /|\
     / | \
    L-----H

Since the measured time difference is between 0ms and 10ms, the reality is probably somewhere in between these two extremes.