Even though you are paying for a record to be made, you do not have control over that record. The doctor can note whatever they want, even if it is not really what happened. You do have the right to dispute your record, but without a solid contradictory record, you will have a hard time doing that.
Besides being able to write whatever they care to write in your record, the doctor can redact information at a later date. So the record is subject to change, again, outside of your control.
Why should you care about what the doctor does with the record they make, own, and keep outside of your control? Sometimes what happened previously really matters. Some possibilities are insurance disputes, malpractice events (which you think will never happen to you, but may), recommendation of procedures requiring a second opinion, and ability to donate blood or organs.
Perhaps the best reason to keep your own record of your medical care is your health. You spend more time with yourself than anyone else. You have the opportunity to track data related to medical visits as well as everyday events.
One extreme example of tracking everyday events is diabetic care. Diabetic people must continually evaluate blood sugar levels. Relying on a doctor to do that is not a realistic option for maintaining good health. In this case, use of control charts would provide valuable data on which events/foods/etc. affect blood sugar levels the most. Lifestyle adjustments could be made based on the data collected.
Another example of event tracking would be control charts for weight. Exercise and diet could be included for additional decision making ability.
Just tracking your own immunizations could keep you out of the office for the occasional tetanus shot that you can't remember if you need or not.
Control your own data. Control you own life.