I… don’t think that’s true.
I’d expect to get convicted if I make a (reasonable) confession of murdering someone who vanished, even if there is no single other bit of evidence.
Not if you made that confession outside of any prosecution process and then withdrew it saying you were just making shit up, I wouldn’t think.
I would expect that to be true as well.
For some reason I can’t really explain anymore, I was thinking of a situation where the confession is made, and reiterated at every step in the prosecutorial process, without any other evidence (for or against) being available for the process.