This weeks patch notes supposedly fixed the receiving of rewards from completing a random dungeon via the grouping tool
@ZOS_GinaBruno @ZOS_JessicaFolsom
Fixed an issue where the Daily Bonus Rewards granted through the Grouping Tool would not be granted upon completion of a dungeon.
If a group of 2 or more queue for the random only the player that was the group leader when entering the queue receives the reward. Until recently everyone in the group that queued for the random dungeon received the reward. I have not seen anything that indicated that Zos intends this reward to be only for those who queue and play this solo.