Silhouette Studio (at least up to version 3.5.7) automatically groups together all layers of the same color on import. While this is great for simple SVGs where no layers of the same color overlap, it unfortunately means one has to manually ungroup them when they do overlap. Follow these directions to fix:
1. Open the .SVG in Silhouette Studio
2. Pull apart layers. As you do so right mouse click on each layer and choose "Ungroup".
3. You will see A subtle but secondary box appear on images where there were grouped items as in image below.
4. Continue pulling items apart and ungrouping them. In the case of the image pictured below, what looked like 4 layers is actually six.