Not necessarily, if the token is tied to your public key, but it's a trade off, you need to trust the payer and the mint. Everything is a trade-off

nostr:nevent1qqsf2wk6wqv7khptp69s8gamegq55md883ag2p0wnr9qsrp5cdrzg5qppemhxue69uhkummn9ekx7mp0qgs9pk20ctv9srrg9vr354p03v0rrgsqkpggh2u45va77zz4mu5p6ccrqsqqqqqpkxxlvr

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not the payer, just the mint

How can you know that the payer isn't giving you a fake token?

You check the DLEQ proof the payer includes in the token (which is a proof that the signature of the mint is correct):

https://github.com/cashubtc/nuts/blob/main/12.md

Relevant section: Carol (another user) verifies DLEQ proof

it's a neat little trick. the DLEQ's original purpose was to prevent tagging by the mint but we noticed that it can also be used to make the signature publicly verifiable.

Tokens tied to public keys can be used to censor individual users even without KYC.

You could defeat this by using an ephemeral, one time use key pair for this transaction.

But some users lock it with their nostr keys.