Reverse engineering the software in auto computers is difficult but doable. There are several companies doing that today in order to allow users to reprogram timing and engine control parameters. Eliminating the recording function would be possible. However, I would suspect it would be both expensive (reprogrammers cost as much as a new computer 4-600 dollars) and possibly illegal. Tampering with or disconnecting safety systems in a car carries a hefty fine and in some cases jail time.
Many people would buy a replacement non-tattle CPU if it were available. It would be like wiping Windows from your PC and installing Linux.