I wouldn't say they are disproved, just not substantiated to the extent that Hal should have used it.
TruthOrFiction.com's conclusion is that when all is said and done, there is not enough good evidence that the story is true. We stop short of declaring it fiction, but regard it as not sufficiently proven. The report about Darwin's change of heart comes from one person, Lady Hope, an energetic Nineteenth Century Christian, while many members of Darwin's family denied it and there is nothing from Darwin's friends, colleagues, his own statements or writings to substantiate it.
I would. Mrs Denny was a liar. And truthorfiction.com are just trying to "wardrobe malfunction" this.