Man, I've been reading all these posts and it's some deep stuff indeed, I wouldn't really call Frodo "mad", I feel a better word would be "traumatised", I think it's quite clear to see in the book as after he destroyed the Ring he used to finger and hold a white pendant that hung around his neck (I'm not 100% sure of all the details of whether or not it was a pendant or a jewel so please correct me if I'm mistaken), this sounds like the acts of a deeply disturbed mind albeit one that is not completely mad.
As for Frodo making everything up in a sort of delerium, I'm not entirely sure what to think although I hope it wasn't as I like the real story better.