Yes, it can touch on it´s own (called ghosting). There 3 possibilities that could cause your problem.
1. broken Connector ( measure connections between connector and) logicboard)
2. Broken Touch IC/Broken solder points (replace the touch IC on the logicboard)
3. defective or low-quality Display (test the Display you installed on your customer's phone on a phone with working touch and test if the ghosting continues
But all in all this problem can be hard to fix because the phone was thrown. This hard acceleration can cause many defects on the logicboard, for example, defective solder pads or points or small cracks in the connection lines (which can cause temporary defects depending on the temperature of the logicboard)