Who told you that if you purchase USDT or TUSD, you don't have anything to worry? As far as I know, there is no stablecoins out there, which can be trusted. The recent Bitfinex scandal proved that USDT is no longer backed up with real assets (at least not 100% backed up). None of the stablecoins that are currently circulating in the market has completed an independent third party audit of their assets.
Now the Binance USD coin is going to be even more risky. Because it is associated with an exchange. If there is a major hack (Binance was a target of several minor hacks in the past) and the exchange incurs a loss, then this coin can lose its value very rapidly. I am not going to trust any cryptocurrency other than Bitcoin, be it stablecoins such as USDT or altcoins such as ETH.