So insulin certainly enables the uptake of glucose into our cells, but it also acts as a signaling hormone. When your dietary sources of glucose run low, the normal non-diabetic will lower their insulin levels and raise their glucagon levels to signal the liver to produce glucose (gluconeogenesis). When your insulin levels are too high, you actually suppress this glucose production further causing hypos. This same effect occurs with alcohol which is metabolized by our livers, gluconeogenesis is suppressed and we can suffer a hypo.
And Sally is right, fat burning (ketosis) is suppressed with higher insulin levels. But during ketosis fat is converted to ketone bodies (by our livers) and our cells actually burn ketones rather than glucose.
I've never been really confused by the hypo thing, what has always confused me is my son. He sits there, eats 250g of carbs in a sitting, has presumably normal blood sugar and insulin levels, yet he gains no weight. Where does all that glucose go? It can't go into his cells, we only store some 300 g of glycogen and he is a couch potato. And he doesn't convert it to bodyfat, he is rail thin. And we only excrete glucose when our blood sugar gets high (> 180 mg/dl), which he doesn't have. Where does it go? That is what I want to know.