Interesting question. Not sure I have actually heard this one before. Unfortunately, you can't make those Ning App tabs visible only to the Network Creator as you can with tabs you create. That would solve this for you. Not sure if this is doable, but hopefully someone has a CSS trick.
Found a work around...
Add ning app - save tab settings
copy app url
add "new tab" - click "link to existing page" choose the app url and save
delete original ning app tab and save
delete "new tab" and save
paste in url of ning app and page shows up!
Well, heck. I hadn't thought of it this way at all. I guess that app will keep working fine. To be honest, I am not sure about this in the long term, but I think you did it. Nice job!