Judith, if you end up in the big tree but have NEVER accepted a merge request, then one of two things must have happened: 1) You accepted one or more collaboratorts at some point and THEY did a profile merge with your tree, or 2) you have invited one or more of your family members to claim their profile (by entering their e-mail address into their profile) and THEY accepted a profile merge or collaborator request from someone.
In other words, the only possible way for your tree to end up being connected to the Big Tree is if you, or someone you have granted permission to, accepted a merge request. It just can't happen in any other way.
The ONLY way to absolutely guarantee that your tree will never end up merged/connected to the Big Tree would be if you NEVER invited ANYONE else to join, view, collaborate or merge. Clearly this would defeat the purpose of building a tree in the first place- which is precisely why Geni is not a good place to attempt to keep an isolated, protected tree.