The stereotype is true, but only for asians who immigrate to North America or any other "western" country that isn't very crowded.
However, the stereotype doesn't really differentiate between immigrants and "native" asians. I drive well. I know I do. However, there are some asian people who appear to drive poorly because their driving style is so different. In many asian countries, it's so busy that you really need to push and shove a bit to survive. You're an ant in a really crowded place, so you need to "fight" a bit to get where you need to go. Same with on the road. Their driving laws matter less. Even when there's only a small space to sneak in between, or a small parking spot, you need to take it.
When they move to North America, they seem completely wreckless, but I don't even think they realise that they appear to be a danger.