The "that" elimination problem
Solution 1:
In a comment John Lawler wrote:
Chuckle is not a speech verb. You can whisper, shout, snap, cackle, or pipe up with a direct quotation like "It's 2 pm", or an indirect that clause; but you can't, for example, *chuckle that it's 2 pm. You can chuckle about something, but not a that-complement. One of the ways of getting a that-complement is the the fact that construction; you can chuckle about the fact that it's 2 pm. But this construction is factive, and commits the speaker to the truth of the that-clause, which they may not be able to afford.