There's subtext to Kirk's line to Rand other than him reassuring her - because the fatal accident was avoidable, and he knew it. It was someone's fault, and that clearly was supposed to come through.
It comes through for me--that someone is Admiral James T. Kirk, hence the stiffness. I guess you think "it wasn't your fault" would have conveyed it better? I dunno--seems a little on-the-nose to me...