Does Arthur Clennam know?

Has biographer Claire Tomalin slipped up in her account of Little Dorrit? In Charles Dickens: A Life, she writes

Arthur Clennam, the unheroic hero, has been brought up by a ferociously pious mother whose creed is 'Smite Thou my debtors, Lord, wither them, crush them.' He discovers that his real mother, who died young, had been a poor singer training for the stage, and so dedicated to the world of art and imagination despised by his foster mother.

The problem is that although we as readers learn this information, via a dramatic revelation scene late in the book, it's not made explicitly clear that Arthur ever does. As the book approaches its climax, Clennam is confined in the Marshalsea debtors' prison, delirious from a fever, and being tended to by Amy Dorrit, the "child of the Marshalsea," who was born within its walls but who is now free. His ostensible mother, an invalid with whom he has long had a distant relationship, is being blackmailed by one Rigaud alias Blandois. In a breathless series of disclosures, we learn that Arthur is the product of an adulterous affair on the part of his father, that his real mother was treated with great cruelty, that Mrs. Clennam's sinister aged retainer Flintwinch has a previously unsuspected twin brother, and that Amy Dorrit is, by a string of improbable circumstances, the rightful heir to a legacy from the Clennam fortune. To force Mrs. Clennam to pay up, Rigaud has sent a letter with the details to Amy and Arthur, with instructions to open it if it is not retrieved by the time the prison bell rings that evening. When she learns of the letter, Mrs. Clennam somehow rouses herself from her chair and hurries across the Thames to the Marshalsea, where she instructs Amy to read the letter and implores her to keep its contents secret until she (Mrs. Clennam) dies. Arriving home, she witnesses the sudden collapse of the house where Rigaud is waiting for her return. Rigaud is crushed to death by the wreckage, Flintwinch vanishes, and Mrs. Clennam collapses in the street. She lives for another three years, unable to speak; we aren't told whether Arthur ever sees her again.

While Arthur slowly recovers, Amy receives a box of documents containing the original evidence behind the revelations. On their wedding day, she presents them to Arthur, but asks him to burn them unread, which he promptly does. Had he read them, he would have known, as he had always suspected, that his family had always been under some kind of obligation to Amy Dorrit, and that his inheritance — if it still amounted to anything — was in part rightly hers.

As far as I can tell, there's just one, almost cryptic, indication that Amy will eventually share part of the secret with Arthur. It comes at the exact moment when she receives the cache of documents:

Little Dorrit came in, and Mr Meagles with pride and joy produced the box, and her gentle face was lighted up with grateful happiness and joy. The secret was safe now! She could keep her own part of it from him; he should never know of her loss; in time to come he should know all that was of import to himself; but he should never know what concerned her only. That was all passed, all forgiven, all forgotten. [Emphasis added]

That is, though the scene won't be narrated in the pages of the book, Arthur will at some point at least be told the true story of his birth. Which may, in part, explain why he is never described as visiting Mrs. Clennam again in the few years that remain to her.