There is no guarantee in that, which is why you will always see some stablecoins quoting a little less than the value of a USD or a little higher than the value of a USD. Most claim that they have their stablecoin backed by the USD, but this is truly not so, and it is due to many factors including their selfish gain in rate manipulation and what you just explained above.
I can only believe that a Stablecoin will always be equal to $1 if the stablecoin has its own blockchain and is truly backed by the USD.
You are correct that that there is no guarantee that stable coin will be always equal to one dollar, because there are various variable assets behind its backing and those keep fluctuating in value such as treasury bills, Bitcoin or any other fiat currency such as Euro or British pound, we exactly don't know what are the real asset being used as collateral to support stable coins are often unclear.