Just bought a fated engram from xur today and I received a exotic weapon that I'm carrying (The Wardcliff Coil) and have had since the first week of launch and no I dont have all the exotics in the game and I still need quite a few.
Whatever exotics you don't have, need to be ones that are available as drops, not Acrius or Mida or Polaris Lance for example. If an exotic is got from a quest of some kind, then it likely is not in the drop table for the engram. If you don't have certain exotic armor pieces, you need to be on the character they go with when you buy the engram.
Otherwise I don't think I've ever seen Bungie acknowledge there are problems with it. So I can only assume problems with it are attributed to not knowing how it works.