couple of things I can think of
first in order to hurt the fish, current would have to flow through them - example: birds perch on live wires all the time, no ill effects unless they happen to come in contact with ground while touching the wire, then poof
by grounding the tank you may actually be increasing the likelyhood of current flow through the water and therefore fish.
electro chemical reactions take place when current is allowed to flow through water. Lets say you have a motor that is not properly insulated, most likely its windings/conductors will be made from copper. If you ground the tank with a metal conductor, one of the conductors (the softer one) will give up metal oxide to the other. One becomes the anode, one becomes the cathode and the water becomes the electrolite. In the marine environment boats have a chunck of zinc (called a sacraficial anode) bolted to the hull to protect other metals on the vessel.
last thing I can think of is that we regularily "shock" rivers and streams around here to count fish. The equipment used produces very high voltage (20,000-30,000volts) to product a tiny current flow through the water. The fish are stunned long enough to identify species and count, pehaps even collect scale and DNA samples. The point is that at 120volts your not going to hurt the fish but you may kill yourself if you happen to be also touching ground.
don't know about the affects of prolonged metal oxides, but I suspect it can't be good for the fish.
Bottom line is if you feel a tingle of any kind, don't worry about the fish worry about yourself and get it fixed.