I'm an American driver who (obviously) wasn't taught this, either. However, I read about it around the same time a bicycle gutter was painted in front of my house, and it stuck with me. As a result, every time I open my car door I think "Dutch Reach!" and I check my mirror for cyclists (I don't actually open the door with my opposite hand). So even if it's apocryphal, it's a catchy idea and you should take the credit.
My full technique also involves popping the door only a few inches and allowing it to sit that way for a couple seconds, then opening it slowly, just to be doubly cautious.
My full technique also involves popping the door only a few inches and allowing it to sit that way for a couple seconds, then opening it slowly, just to be doubly cautious.