Earlier quoted context omitted.
Frax, USDT, and TrueUSD allow people to deposit into bank accounts and mint on eth mainnet or avalanche c-chain now (note: not mint on both places at the same time), neither make the claim that they are 1:1 backed (except for TrueUSD), but they make the claim that if you wanted to at any time (if you meet the criteria) you can withdraw from eth mainnet or avalanche c-chain to your bank account.
When did Tether USDT stop (fraudulently) claiming to have backing assets?
USDT claim (“Every Tether token is always 100% backed by our reserves, which include traditional currency and cash equivalents and, from time to time, may include other assets and receivables from loans made by Tether to third parties, which may include affiliated entities (collectively, “reserves”).”) [1]
TrueUSD claim ("We work with independent third-party financial institutions to provide cash management for the underlying reserves backing TUSD tokens so that each TUSD token is backed by an equivalent amount of dollar deposits, cash equivalents, short-term government treasuries, or liquid investments. To achieve this, a portion of the dollar deposits backing TUSD are held in one or more depository accounts at our Banking Partners whose deposits may not be insured by the Federal Deposit Insurance Corporation (“FDIC”). [2]
Frax claim ("FRAX stablecoins can be minted by placing the appropriate amount of its constituent parts into the system. At genesis, FRAX is 100% collateralized, meaning that minting FRAX only requires placing collateral into the minting contract. During the fractional phase, minting FRAX requires placing the appropriate ratio of collateral and burning the ratio of Frax Shares (FXS). While the protocol is designed to accept any type of cryptocurrency as collateral, this implementation of the Frax Protocol will mainly accept on-chain stablecoins as collateral to smoothen out volatility in the collateral so that FRAX can transition to more algorithmic ratios smoothly. As the velocity of the system increases, it becomes easier and safer to include volatile cryptocurrency such as ETH and wrapped BTC into future pools with governance. ")[3]