HI increases IR, long-term. See Downregulation and upregulation: The Insulin Receptor and Insulin oscillation.
HI doesn't increase IR, short-term. How can I claim this? The above diagram represents a Negative Feedback (NFB) control system, which is how Blood Glucose is regulated.
"Input" represents Glucose from digested sugars and starches. The arrow pointing at AOL represents Blood Glucose (BG). The triangle containing AOL represents pancreatic beta cells. "Output" represents Insulin Secretion (ISec). More BG = More ISec.
The box containing ß represents three things that work in parallel to reduce Blood Glucose.
1) The Liver. More ISec = Hepatic Glucose Production rate decreased.
2) Muscle mass. More ISec = Glucose intake to Muscle mass rate increased, via Glu-T4.
3) Fat mass. More ISec = Glucose intake to Fat mass rate increased, via Glu-T4.
The three things aren't of equal strength, but they provide overall negative feedback.
If overall negative feedback is halved due to doubling of overall IR in the above three paths, ISec doubles. If you don't believe me, see Idealised Negative Feedback Inverting Amplifier using an idealised op amp on WolframAlpha. Double the value of resistance 2 (the negative feedback resistor R2). and the output voltage on the inverting amplifier doubles from -10V to -20V.
The idealised Negative Feedback Inverting Amplifier using an idealised op amp on WolframAlpha is interesting in that an idealised op amp (the triangle with + and - inputs) has infinite gain and infinite voltage on its power supplies. As a result, there is zero volts (output voltage divided by infinity) between the idealised op amp's + terminal and its - terminal. If the idealised op amp's + terminal is connected to 0V (a.k.a. "Earth"), its - terminal is at 0V (a.k.a. "Virtual Earth") and has zero variation, whatever the input voltage. An actual op amp has a voltage gain of ~140dB (~10,000,000), so an output voltage of -10V can be achieved with a voltage of 1uV (one millionth of a Volt) on its - terminal.
If pancreatic beta cells had a zero threshold and infinite gain like an idealised op amp, BG would be zero and have zero variation with varying Glucose input. Pancreatic beta cells actually have a positive threshold and low gain, so BG is positive and has significant variation with varying Glucose input.
If ISec becomes zero (as in type 1 diabetes), there is zero negative feedback and BG goes up a lot. The same thing happens to the voltage on the idealised op amp's - terminal if its power supplies are 0V instead of infinite.
If ISec becomes insufficient (as in type 2 diabetes), there is insufficient negative feedback and BG goes up a bit. The same thing happens to the voltage on the idealised op amp's - terminal if its power supplies are 5V.
Having established that ISec is proportional to overall IR, what would happen if overall IR was proportional to ISec? If ISec doubled, overall IR would double, which would double ISec, which would double overall IR, ad infinitum. ISec would increase to maximum instantly. THIS DOESN'T HAPPEN. Therefore, IR doesn't increase in proportion to ISec, short term.
Long-term, increased ISec increases IR for a variety of reasons, one of them being that increased ISec increases the rate at which cells fill with glycogen. Once full of glycogen, cells must down-regulate their intake by down-regulating Glu-T4 and Glu-T2 (fat and liver cells also up-regulate their output of stuff) or burst.