Yes this issue is STILL happening a year later - infuriatingly (IOS 9.2). I got the 'App is no longer shared with you' message after I had restored a backup from my son's stolen phone onto his replacement phone, when I tried to start a Family Shared paid-for app.
After a couple of wasted hours, including 40 minutes talking to Apple Support, I chanced upon a very simple solution, along the same lines as teerts on Page 4 and others since.
All I did was to download a free app from the list of apps installed by another member of the Family. (App Store => Updates => Purchased). In my case I randomly picked the Ebay app, downloaded it, ran it, and then the problem app suddenly started working.
Kinda embarrassing that it started working while I was on the phone to Apple Support, as at that point I didn't realise what I'd done. Apple Support were helpful in that they spent quite a while with me and treated the problem seriously; but less helpful in that they seemed to have no knowledge of discussions like this on their own forums!
No idea if this will work for others, but hope it helps someone.