GFI basically "senses" a ground or completed circuit after the outlet, instead of one returning to the main service panel, thru neutral, or thru third wire ground. In many cases you could be part of that circuit.
If repairing faulty ground wire connection corrects tripping GFI, there is also problem with neutral, or some miswiring some where.
Third wire grounding mostly protects wiring in home and appliances. Though hopefully ground wire is better conductor to a ground than you are if, say toaster has a short and you are touching it and water faucet at same time. That's why GFI's are now required in kitchens and baths, they trip immediately if current is flowing thru hot but not neutral or ground.
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