Water is not a fuel, it contains no appreciable nutrients. The rest of your post is correct.
As for the OP. long distance running, sub maximal should help improve insulin sensitivity and thus help manage blood sugar more effectively, as would long distance sub-maximal cycling etc. If you are on insulin, you will need to reduce your dose as well or take carbs to offset the increased insulin sensitivity during exercise. I'm not sure how drugs like metformin will help increase insulin sensitivity but you should find out whether you need to modify doses of those as well.
In the absence of any blood sugar lowering drugs, you may find that you can get away without carbs, but you may need a little now and then. If you have the facility, it makes sense to test during exercise to see how you are affected