I think it's fairly simple: Kirk was still the captain, he hadn't ceded command to the M-5. No matter what the computer system was doing, Kirk was ultimately responsible. If the M-5 didn't have a kill switch, that's Kirk's responsibility. If the kill switch didn't work, that's still Kirk's responsibility. Even if there were mitigating factors, that would be something for an inquiry later, not part of Wesley's immediate concerns.