They can! Singing requires either PIN or finger on the fingerprint, and signed "proof" is valid for like 60 seconds. This whole end-to-end attestation with play integrity is supposed to make setting up token-as-a-service things impractical.
> What's going to stop the government from keeping all the salts they're issuing and then mandating that site operators add the salts to their existing logs?
> How does the math say no
BBS+ signatures. Hashes you receive from the government and hashes you send to the site operator are different and not correlated.