You know, the title could be interpreted a different way:
Captain's log. After our battle with the Klingons, the damaged warp core is losing containment. The only place we can reach in time is the nearby computer ruled planet Mechanista, where they should be able to fix the containment fields in time to save the ship.
Spock: Captain, we are in range of planet Mechanista.
Kirk: Uhura, open an emergency channel.
Uhura: Aye, sir.
KIrk: We have an emergency. Warp containment fields failing. Containment breach immanent. Need repair crew beamed aboard immediately.
Mechanista voice: We will help, repair crews assembling. Which ship is this?
Kirk: This is Captain James T. Kirk of the United Star Ship Enterprise NCC___
Mechanista voice: KIrk, of the Enterprise?? Kirk the destroyer of computers? Red alert! Red Alert!
Spock: Captain, the planetary defense system is powering up!
Kirk: Full power to the shields!
Mechanista Voice: Fire! Fire! Death to Kirk!
Yes, the title could be interpreted as asking about Kirk's reputation among computers.