Twilight,
Hubbert works well for USA oil, but by your definition, it is not entirely "natural".  For geopolitical factors, many areas were placed out-of-bounds for environmental reasons. There were many innovations integrated into the production data.  Even with the major recent discovery, the North Slope, the older estimates project forward fairly well.  

For USA oil, Hubbert seems to cope well with most of the "unnatural" factors that you mention.   Going global, politics will probably throttle production more than disasters.  New discoveries probably won't be as significant for the world as for the USA.  It is likely that we will need some stupendous additional innovation just to match the innovation embedded in the USA models. This reasoning implies less global URR "loft" and global depletion rate "depression" than we see with the USA models.

Yes, I guess that's why I suspect that the Hubbert model will work, because even in this example, where we did indeed have all of those issues, it still works pretty well.  That tells me that you'd really have to "monkey" with things a lot to get to the point where the errors are really big.  I think it's just that the effects of the really big fields swamp out everything else - combining with smaller fields of similar shape just shifts the curve a bit.  As goes Ghawar, so goes the world.