Could you clarify what you mean when you say "oubliette"? To me an oubliette is just a french word for a prison dungeon which, while a lot more rare than people tend to think, were definitely real.

However there is also special prison cell kind of "oubliette" which was allegedly some kind of special cell were people were meant to be locked up forever and forgotten. This kind is featured in a lot of works of fantasy but to my knowledge never actually existed.

Here's an account of oubliettes and other fun French durances vile. There seem to be variations, from places where you were thrown in and forgotten and died slowly, to places that had waist-deep water, where you were thrown and forgotten and died pretty soon. The general impression is that Louis XI took great delight in seeing his opponents tortured and generally made to feel unwelcome, in line with the theory of justice as revenge upon the criminal.

However , I would not take Arthur Griffiths as a reliable source. The Wikipedia bio of him, ( taken from the Dictionary of National Biography) says "His later accounts of crime and punishment in England were sensational and grotesque, designed to appeal to the baser fascinations of his Victorian readers" and this has plenty of that... but it's at least a collection of what seems to be the legends.
Violet le Duc and others questioned the great number of "oubliettes" found in castles , pointing out that many of them probably were simply cesspits and latines. But he did conclude that they existed in the Bastille, and in Chinon and Pierrefond castles. Here's the article in French discussing it...pointing out that people tended to see bones from an old kitchen as evidence of it being a torture chamber, etc.