To Prevent Insulin Resistance Potassium Supplementation is a Must on Protein-Modified Fast W/ Out Fruits & Veggies

You don't need supplemental K, well... unless you are on a protein modified fast without fruits and veggies ;-)

The 1984 study by Norbiato et al. is not a very recent, but it's probably a very important study which was set up to investigate "the role of potassium deficiency in the development of glucose intolerance during caloric deprivation" (Norbiato. 1984).

Or, put simly, the scientists wanted to know if a low potassium level may promote insulin resistance and modify or is modified in response to dieting (in this case protein-modified fasting). In the study, two groups of subjects were studied. The "normal" group consisted of ten subjects, who were 27-45 years old and whose body weights ranged from 89 to 115% of the "ideal body weight". The "obese" group group consisted of twenty subjects aged 21-48 years who were 70%-131% overweight.
Before the obese subjects were put on a protein modified fast (PMF) all subjects, lean or obese, received a "weight-maintaining diet" with 200g/day carbohydrates for 8 days.

Figure 1: Macronutrient composition of the ~380kcal PMF diet (Norbiato. 1984).

"The diets were calculated according to individual tastes, employing varying proportions of egg white, beef tenderloin, skim-milk cheese and water-packed canned tuna. For the PMF, total calories varied from a mean of 350-399 in individual subjects, with a mean of 378+/-36 (SD) 

[...] Calculated protein intakes, according to standard tables, were 70.8+/-7.6 g/day (about 79% of calories). Calculated fat intake was 5.7+/-3.5 g /day (19% of calories). Carbohydrate contributed 3.2+/-1.3 g/day, 2% of caloric input" (Norbiato. 1984).

As far as its potassium content is concerned the PMF diet was (as probably most diets that are almost exclusively protein) on the skinny side (15 +/- 3.9 mmol of potassium/day | adult men and women should get 100mmol/day and 72mmol/day, that's 3,800mg and 2,800mg/day or 8-9 bananas if you want to "go bananas" instead of leafy greens ;-). Nevertheless, only 10 out of 20 of the obese subjects received an oral potassium chloride (64 mmol/day) supplement (KC1-retard, Zyma, Italy). The other ten patients received identical placebo tablets.
Interestingly, the potassium levels dropped in both groups during fasting. More importantly, though, the decrease in potassium was associated with a sign. reduction in peripheral levels of insulin along with an increase in insulin receptors and a striking reduction of peripheral glucose utilization in the obese subjects on their protein modified fast.

Figure 2: Mean integrated area under the glucose tolerance test curve in obese subjects submitted to protein-modified fast (PMF) with or without oral KCl supplementation (K): studies were performed in the control period after a 14-day fast and after after 10 days of refeeding with a diet containing 700 kcal (45% carbohydrate) per day (Norbiato. 1984).

Increase in insulin receptor binding and impaired glucose management? How does this go together? Well, if the receptor does not respond, it is no wonder that the researchers found that their subjects ability to handle glucose was significantly impaired in the euglycaemic clamp study.
References:

• Norbiato, Guido, et al. "Effects of potassium supplementation on insulin binding and insulin action in human obesity: protein‐modified fast and refeeding." European journal of clinical investigation 14.6 (1984): 414-419.
• Rowe, John W., et al. "Effect of experimental potassium deficiency on glucose and insulin metabolism." Metabolism 29.6 (1980): 498-502.