Not exactly. The hypothesis that gravity waves travel at the speed of light is used to calculate the direction of arrival, or rather the cone of arrival. The difference in the time of arrival is given by:
dt = D x cos(theta)/cThe time of arrival constrains the source to lie on the surface of a cone, whose "cone half angle" is equal to theta. If dt x c / D is greater than 1.0, then, either the signal received at the two stations is not from the same source, or gravity waves are slower than the speed of light. If dt x c = D then the source lies along the line joining the two stations, if dt = 0, perpendicular to it.theta = acos( dt x c /D)
where:
dt is the difference in time of arrival
D is the distance between the two stations
c is the speed of light
theta is the angle of arrival off the line joining the two stations.
Your point is valid. Notice that I didn’t say it proved that gravity waves travel at the speed of light, only that it indicated they travel at the speed of light.
Perhaps I should have said it was consistent with the ‘assumption’ that they travel at the speed of light.