It can happen, but luckily rather rare for me personally though.
I figured it was because when unlucky and punching the needle as you say straight into a nerve bundle of some kind.
If it happened in the thigh it feels much less intense than what it can feel like if your unlucky with you punch into the stomach region. Here they can be really very very intense type of pain. That is the type of pain from the needle punching through a nerve bundle. Then you also have the other type of pain that can come from the insulin you blow into a sensitive tissue area. That I tend to experience can have a longer effect for hours but more like a burning sensation, while the first type typically goes away after just some minutes but is more like intense knife-cutting pain.
Some in the stomach also result in a rather big blue mark, so must be when we puncture through a vein, which also can bring along some sustained type of pain.