Do I Need to Document the Termination Meeting?
Yes. Documentation of the termination meeting is important, regardless of the reason for termination. Actually, documentation of termination due to a serious rule infraction may be more important than documentation of a termination meeting due to continued poor performance. Assuming that the incident is serious, necessitating immediate termination, you will want to write up the incident, information obtained in investigating the situation if you were not present when the misbehavior occurred or was discovered, and the reasons for choosing to terminate the employee rather than take other action, like suspension.
You can never be sure, regardless of the rule infraction. Even the worst-behaved employee may later file a lawsuit or a claim with an investigative agency such as the EEOC, claiming the decision was prompted by bias.