Give your boss the fact based version of what actually happened. That the call to you happened while he was running a personal errand. That when you called him for advice/support, he recommended that you reboot a server. Say that you were unwilling to reboot the server given that you were unable to reach anyone within the department to coordinate the rebooting of the server with. You eventually reached the hospital supervisor who stated that they wereshe was "taking point" on this issue, you logged the incident and left it at that. If simply stating the facts amounts to office politics to you, then there is nothing we can do for you. You cannot afford to leave your colleague's self-serving narrative to stand on its own, unchallenged. Not if you want to preserve credibility with your boss or even if your colleague, who probably needs to know that he cannot say anything he wants and expect to get away with it.
I am wondering why you did not notify your boss nor did you follow up with your colleague when it was clear to you that you couldn't reach anyone in the department to coordinate the rebooting of the server with. You are not mentioning what you found when you checked the server logs for two hours but it looks like you found nothing. Your boss and your colleague should have known that you were unable to coordinate the rebooting of the server within say 30 to 60 minutes of you reacting to the incident.
You should have gotten back to your boss and your colleague when the hospital supervisor said that they wereshe was "taking point" on the incident. Because the incident was clearly unresolved from a technical point of view since the server had yet to be rebooted.