I'm not sure as to the exact pathway(s) but it's a response to the increased blood glucose/reduced insulin sensitivity. Just like Type II diabetics have high insulin because normal insulin isn't doing the job.
There's a graph in this paper showing what happens to glucose, insulin etc with low dose GH therapy.
http://jcem.endojournals.org/cgi/content/full/88/4/1455
As I understand it, insulin and HGH are opposing hormones. Naturally, you can have one or the other with insulin taking priority. Meaning that if you eat high glycemic carbs it will always stimulate insulin production and suppress HGH, which is one of the reasons you shouldn't eat ice cream just before going to bed.
I had a test done on me when I first went to an endocrinologist for HRT. It was called something like and insulin hypoglycemic test. The test was to determine my insulin sensitivity. I had two nurses and one doctor in the room. They injected me with insulin in one vein in my right arm and when I would start to pass out they injected dextrose in the vein on my left arm. There was an inverse relationship between blood sugar, determined by insulin levels, and HGH production. When my blood sugar was low, HGH spiked. When they pumped dextrose in my blood stream HGH dropped.
Type 2 diabetes, a huge problem in Hawaii and ranked one of the highest in the nation, is caused when you constantly are producing insulin. That occurs when you are constantly eating and snacking on primarily carbohydrates which we do a lot of in America. We are always eating. Eventually, because you are always producing insulin, you start to develop a resistance to your own insulin and have to produce more and more to process a given gram of carbohydrate. Virtually everybody by the time they are forty have some form of insulin resistance compare to when they were in their teens. Not enough to be type 2 but resistance none the less. In the case of my aunt, she was so insulin resistant that her pancreas had to work far beyond normal and eventually "burned itself out." It went kaput and then she became a type 1 diabetic and had to take insulin shots throughout the day and with every meal.
There are some who advocate taking low dose short acting insulin prior to every meal to give your pancreas a break. I guess that sounds good but it also sounds like quite a hassle.
What I don't understand is how HGH causes insulin resistance. HGH will not suppress insulin but insulin will suppress HGH. If immediately after a high intensity workout, which studies have shown stimulate HGH production, you have a high carb drink it will suppress the HGH you stimulated. It is better to stretch out after a workout for about 20-30 minutes before eating anything. That way you keep your blood sugar low and conducive to a GH producing environment.