I've figured out why, when queuing for a "Random" dungeon as a party of 2 or 3, some members are NOT getting the rewards for the random. And it all comes down to where that crown goes after you've queued... here is why, @ZOS_GinaBruno - please pass this information on so it can be fixed.

1) Queue for Random Dungeon solo - get reward 100% of the time (unless the group auto disbands, which is a feature of the broken group finder tool)
2) Queue for Random Dungeon as 2 OR 3 people in group and the crown remains with YOUR party leader - get reward, the "activity" is considered to be a RANDOM dungeon for both of you.
3) Queue for Random Dungeon as 2 OR 3 people in group and the crown does NOT remain with YOUR party leader but instead is with one of the "strangers" you've joined - Reward will likely NOT be given, depending on THIS factor - did the "stranger" also queue for a Random? If they did, you will get the reward. However, if they queued for a SPECIFIC dungeon, the activity is considered a "SPECIFIC" dungeon and the ONLY person to get credit for a Random would be the original leader of YOUR party who queued for the "Random" dungeon.

I hope this makes sense... basically, the game programming is punishing anyone trying to run a random in a pair - you're better off getting into a group of 4, or queuing on your own. This kind of sucks, because its a huge deterrent for husband/wife playing combos like my wife and I. It's basically making us run TWO dungeons, whereby we both queue as crown each time, to get the job done.