Yes, you can invite people to join your storytree. To invite them press on the share icon in the upper left hand screen. Then press on the invite button on the upper left part of the screen. Once people are members of your storytree they can add stories and they will appear in the tree where you will able to view them.
I understand that. My problem is that when they view the story from the email invite, it opens up the web browser to the site where they can only add text, not video. My daughter installed the app after I added her and she can't get to my story from her iphone app.