I have tried to get the quest a second and third time on alternate characters and when I open the chest I get nothing. Sorry if this has already been reported.
Update: Going to try this week with another key to see if patch fixed this issue. Also got the thorn quest for a third time has not duplicated. This would appear to be the only outlier.
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Reported this some time ago myself, my theory is bungie intended the quest to lock once per character to prevent repeating the quest over and over to farm exotic shards but has resulted in the quest locking to once per account.