Not necessarily problem solved.
He stated that the safety was engaged when this has happened.
If the safety is functioning properly, then the hammer will not fall. If that is happening then the trigger group has nothing to do with the issue as OP is sure the shooters finger is off the trigger too.
The safety on the 870 only physically blocks the trigger only, not the hammer or sear. The hammer can still fall if the sear fails to properly engage the hammer. Check the hammer and sear engagement and the sear spring. With the trigger pack out of the gun see if you can force the hammer off the sear without pulling the trigger. Also look for wear or rounding of the hammer hook and sear.
Could also be an obstruction in the firing pin channel or broken return spring causing the firing pin to be extended beyond the bolt face.