Birch tree

I was told years ago that it was a Silver Birch. Looking up Silver Birch on the web is giving me doubt. I'd like to know for sure. At the time it was 3 or 4 feet tall. The woman worked at a garden center so I had no reason to doubt her. She also said I was growing it like a bush and I needed to prune it. Well I did every year till I couldn't reach the top. Every year I'd cut the lower branches and the next layer of branches would grow towards the ground. I like it. When I told someone what it does they said the roots like to be shaded. As you can see it's very round. I always pruned it to the natural shape, so I'm thinking this is how it is suppose look . It looks awesome during a full moon.