If you look at say Lucy on profile view you will see
Added by: Greg Haefele on October 12, 2010
Which is probably before you joined Geni & he is probably a cousin.
If the data is correct can you try merging? Then you can control the privacy at merge time (I think). If I merged for you it will probably default to public & you (only - as a family member) would have to re adjust the privacy setting anyway. So maybe you can try it yourself? Just drag & drop one profile on top of another.
It actually shouldn't matter much but I think the best way would be to drop Greg's on top of yours. Then in the merge carousel, your profile should show to the left, making it the "main" profile. When the merge is successful there may be a "conflict resolution" - both "tree" and "data." For the tree it will show as yellow triangle - let the tool guide you. If the data conflict resolution screen doesn't pop up after that (its tempermental in showing up), you can check from profile view, actions menu - if there aren't any it won't present. I suggest looking anyway though because you will want to progress to the next screen, edit basics, and search for the little radio button on the upper right hand corner. It should show you "this is public" - and then you can DE select it to make it private.