Some of the stories quote National Grid as saying that the driveway, water and sewer lines are on their easement, but don't say that the house is.

Nobody has said that National Grid has sent out a surveyor. Which leads me to suspect that they don't actually know whether the house is on their easement, in which case the statement reported in other stories that they are claiming the house in on the easement is either erroneous reporting or posturing by National Grid.