Please forgive my pushback but:

No third party: Almost certainly as a user there are still third parties involved, this isn't (AFAICS and based on other discussions) a user facing chain (edit: correction, they do say the chain is public, but here I really mean user facing value: you aren't minting stablecoins, you have to get them from somewhere). At "envisioned" transaction rates you would in practice not be syncing the chain and interacting with it yourself in any meaningful way.

Settlement: chain settlement is different from financial settlement. Between clearing ends there will still need to be sufficient demonstration of KYC, exchange of some form of actual holdings and so on. Typically the attraction of /to stablecoins is that they're used to perform transactions ahead of movement of actualizable value in target currencies. A possible alternative model is that all invested parties sink actual value into a global sink fund backing the stablecoin that is sufficiently protected to ensure that it does not devalue. In practice organizations almost certainly aren't going to part with wealth on those volumes and will operate secondary private exchange markets and settlement in bulk to escape concerns of short term loss, leverage, inflation and many other dynamics.