Bug still present in patch 1.11 - I'm very sure I found the cause of this. As it appears, the quest gets automatically completed if you have looted a particular Hidden Treasure chest prior to discovering this quest.
In my case, I have looted the body and the quest "Hidden in the Depths" appeared in my quest log. As the recommended level for the quest was too high for me, I decided to come back to the cave after I'm higher level.
Then, a few days later, the quest completed by looting a random Hidden Treasure chest south of Ard Skellig - the one between Kaer Muire, Fyresdal and Elverum Lighthouse.
I'm thinking this Hidden Treasure chest is somehow linked to the Hidden in the Depths quest. I hope this information will lead CDPR into the right direction to fixing this bug.
Thanks,
Adrian