[Kalimac]

Well, among other things Gandalf probably said something along the lines of "Congratulations, it's over. Thanks, by the way."

I agree with Child; Tolkien himself said that Frodo would have told the truth, and besides after an experience like that he would probably be beyond dissembling. He's already a shell of what he was before; his character has been stripped down to its essentials by what he went through; what possible pleasure or advantage could he take in having people believe that he did something which he couldn't? Lying about it would have made him feel worse about it than he did. It's like going through a very long, very hard illness and then finally taking a turn for the better. All your strength has been sapped by fighting the disease, and now that you're finally getting better you have no energy left to care about anything except recovering. There's no room in your brain for calculation of petty advantage; if someone asks you a question you'll tell them the honest answer, because it's the easiest and simplest thing to do.