Gluconeogenesis could explain why some low carbers have stubbornly high FBG.
But the proposed remedy of increased fat intake doesn't explain why a low
carber I know who typically gets 80% of his calories from fat is unable to
get his blood sugar below 90 mg/dl. Another possibility is that his pancreas
is permanently damaged, but he seems to think it's fine.

Yet another possibility is suggested by this study I found. It may help
explain both why low-carbers tend to have lower FBG than high-carbers as
well as why some low-carbers cannot get their FBG down to "optimal" levels.
According to this study, a diet rich in monounsaturated fats improved
insulin sensitivity over diets rich in either carbs or saturated fats. So
just eating more fat than protein may not be enough--the types of fats may
also be important. The low carber I referred to above does eat lots of SFAs.

One question the study didn't address is whether different types of
saturated fat make a difference. For example, saturated fat from grass-fed
animals or coconut oil versus grain-fed SFAs. Another question it doesn't
address, is whether chronic mildly elevated FBG (83-99) is damaging.

I know that pondering these things breaks the taboo against speaking or
thinking ill of saturated fat, but I am interested only in the facts, not in
unthinking devotion to any nutritional dogma, whether it be pro-SFA, or
anti-SFA, or any other. I recognize I cannot possibly please everyone, and I
therefore don't try to. Please keep in mind that I eat way more saturated
fat than most people, so I am not an anti-fat fanatic by any stretch of the
imagination.

Here are relevant excerpts from the study:

A MUFA-rich diet improves posprandial glucose, lipid and GLP-1 responses in
insulin-resistant subjects.
    Paniagua JA, de la Sacristana AG, Sánchez E, Romero I, Vidal-Puig A,
Berral FJ, Escribano A, Moyano MJ, Peréz-Martinez P, López-Miranda J,
Pérez-Jiménez F.

    Lipids and Atherosclerosis Research Unit, University Hospital Reina
Sofía, Córdoba, Spain. [log in to unmask]

J Am Coll Nutr. 2007 Oct;26(5):434-44.

... Fasting serum glucose concentrations fell during MUFA-rich and CHO-rich
diets compared with high-SAT diets (5.02 +/- 0.1, 5.03 +/- 0.1, 5.50 +/- 0.2
mmol/L, respectively. Anova < 0.05). The MUFA-rich diet improved insulin
sensitivity, as indicated by lower homeostasis model analysis-insulin
resistance (HOMA-ir), compared with CHO-rich and high-SAT diets (2.32 +/-
0.3, 2.52 +/- 0.4, 2.72 +/- 0.4, respectively, Anova < 0.01). ...
CONCLUSIONS: Weight maintenance with a MUFA-rich diet improves HOMA-ir and
fasting proinsulin levels in insulin-resistant subjects. Ingestion of a
virgin olive oil-based breakfast decreased postprandial glucose and insulin
concentrations, and increased HDL-C and GLP-1 concentrations as compared
with CHO-rich diet.