You're thinking of a dying declaration which is not the same as a deathbed confession. http://en.wikipedia.org/wiki/Dying_declaration
My evidence professor said it is the same, as does the FRE "The declarant’s statement was made while under the belief that his death was imminent"
Just because it can be used as evidence doesn't mean it's true. And just because he wanied until the end of his life to say anything doesn't give it any more creditability or validity than if he had said it 10 years earlier.
For 43 years they said, "I don't care how many thousands of pages of evidence you have. You have no smoking gun, no confession, no name." Then, came forth the head of the Plumbers. He confessed to being part of it. Then they said, "It was only E. Howard Hunt? That's nothing, any bum in the street can confess to anything. I don't care whether you have a taped confession from the most famous person known to have been involved in similar secret matters. Now, I require corroboration, written documents, a second witness, a TV-worthy motive involving sex, and...well, I'll think of more if you find those."