'All but certain' means he (the inspector) is as close to certain as possible without being completely certain. After all, he is not a doctor and is therefore not qualified to declare somebody dead. You are getting confused with another structure - 'all + noun + but' - e.g. all the guests but Kevin brought gifts. Here, in this structure, 'but' means except. In your idom, 'all + but + adjective' it does not. Similar sayings are - all but decided, all but finished, all but won. All mean as close to this adjective as is possible without being completely there.

It sort of does mean mean "all, with the exception of being certain". It means you almost completely agree, but for some reason you are hesitating to say you are certain. You can think of it as saying "I'd do everything but say that I am certain", even though no-one would ever say it that way. Examples might be: "I'm all but certain I passed the exam" "Im all but certain that Green Bay will win the Superbowl this year" etc...

"I'm all but certain.." Is just a fancy way of saying that you are UNCERTAIN about something. "I'm all but certain that war is a positive thing." = "I believe that war is bad." basically. If you look at it carefully, it's basically saying that you may feel ANYTHING else in the world BUT certainty. EXCEPT certainty.