I'm trying to understand how privacy in Monero compares to shielded transactions in Zcash. I understand that with Zcash's zk-Snarks, there's no information about sender, receiver or amount.
I think I understand that with Monero, these data are visible, but obfuscated with "ring signatures" that basically add a bunch of noise so an observer can't detect the signal from the noise. The dancing analogy is that you'll see "me" dancing with many people, but most of what you see isn't really me, so you can't prove that I danced with any one of them. Is that about right?
If so, my question is this: can an observer prove that I didn't pay (or dance with) some recipient X?
I get that the noise might include me dancing with X in which case they cannot disprove it. But what if amidst all the signal and noise, none of it suggested that I might have paid X. Does that not then prove that I did not pay X?
If that is correct, then that certainly seems like information disclosure that makes zk-Snarks superior in privacy.