The issuer just creates a valid transaction and deliver it to creditor. Indeed in 99.99% of time they do not need to record their money transfer on Bitcoin blockchain!
ok. lets say Bob owns 1 bitcoin and signs a valid transaction but sends it to you privately without settling it on chain. now he has SABU tokens, right?
so how are you going to prevent these two scam scenarios:
1. Bob spends his SABU tokens, for example buys a car, and the SABU transaction is supposed to be fast. then immediately he spends the same 1 BTC UTXO that was never settled on chain or even broadcast to the network so he takes his 1 BTC back too. now the initial "valid tx" you had is no longer valid.
2. You never send him SABU tokens but instead broadcast his transaction which will confirm. now he is both out of BTC and SABU.