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Disclaimer: I haven't actually read Chaum's original paper yet. My knowledge is derived from reading the cashu specs (called 'NUTs'). So I can't speak to Chaum's original design.
In Cashu though, the proof Z is not verifiable by anyone but the mint itself. In order to prove a token was indeed issued by the mint, either:
  • the recipient of Z must ask the mint to swap the ecash out, thus verifying its authenticity in the process
  • the mint must supply some extra information to allow offline verification of Z. See NUT-12 for that.