I know that might sound stupid and it really is but I spent recently a few hours trying to figure out why the Search Engine wasn't working fine when queried from my App.
It turned-out that I forgot to ask the permission to use it. So, I was missing this line in my AppManifest.xml:
While this is very stupid, this little distraction made me realize that the system isn't behaving as expected. Indeed, one could expect that the App Model throws an exception such as "Attempt to perform an unauthorized operation" but it doesn't. It's actually even querying the Search Engine successfully but simply, no results are returned.
It is behaving as if it was applying some kind of security trimming but it's not because the App had full control over the site collection...Morality, just don't forget this line and you should avoid some headaches :).