The same argument could be applied to the force of electromagnetism, but electromagnetism conclusively propagates at the speed of light.
Van Flandern also now insists that electromagnetism propagates at infinite speed. (Not electromagnetic waves, mind you, but the field...whatever the devil that means.) It's nonsense, but he's forced into it by his own (mistaken) geometrical argument.
Presumably this frees gravitational waves (as opposed to fields) to propagate at c.