The interviewee is talking about ice on land (Greenland and Antarctica), not about ice in the ocean. If the ice on land melts, then those water molecules migrate away from Greenland because they drop to sea level. That loss of mass would happen regardless of the gravitational pull of water 200 km away and would change the gravitational gradient of the water 100 km away.

Another way to think of it: there's not an "equal" weight of water above Greenland because it's raised above sea level by the land. The weight of rock underneath the ice sheet needs to be included as well.