Galvanic corrosion is caused by dissimilar metals touching like iron and copper.
What metal is the ground clamp connecting the ground wire to the copper pipe made of?
Is the pipeline all copper or are there non-copper fittings, hangers, or anything else non-copper touching the copper pipe?
An electrical appliance could be malfunctioning and "leaking to ground". Also there is a thing called a "ground loop". This is a small electrical current which flows between two different ground sources. To find either of these, a qualified electrician could disconnect the ground from the copper pipe and measure between the two with a meter. WARNING! This could be very dangerous if an electrical appliance is malfunctioning as full line voltage could be present between the ground wire and the copper pipe!
Then natural gas companies connect electric wires to their old metal gas lines as part of their "cathodic protection systems". I suppose this could be another source of current to consider if the supplied gas line is metal and is in some way electrically connected to the water line.