I'm the original reply on this line of questioning. Over the years since I replied to the original question, many, many functions have changed on Fusion. Develop a process for doing anything and you are but one software update from that process not working anymore. Lately, if I want to move anything around in the browser tree, I do the following:
1. In the Browser on the right, right click on the top-most (master) component.
2. In the drop down that appears, click the item at the bottom, "Do Not Capture Design History."
3. In the box that appears, choose "Continue."
4. You now have drag and drop capabilities for most of the components in the Browser Tree.
5. When you are done, right click on the top (master) component in the list and choose "Capture Design History."
Of course, this makes a break in the capture, but you are able to do all sorts of things with the capture turned off that otherwise are impossible. As each of us uses this fabulous software to perform very different functions, this suggestion may or may not work for you.