You dont disagree with the author. The key phrase is "given the choice" from the consumer perspective. That people who sell will demand the stronger if they have the option isnt surprising.
Gresham’s law applies when the seller is bound to a certain rate of exchange between the two currencies. The buyer will therefore pay in the currency she has the least desire to hold for the long term. As a result of everyone doing this, over time all trading will be done in the less-desirable currency.
In practice, you have to settle debts in the government dictated currency. Here Gresham takes hold, the valuable currency will disappear from circulation. Think silver dollars in the US with a higher material value then the nominal value. You still have to accept payment in any dollar so you wont spend silver dollars doing so. As long as you have the choice to sell it for material value. Think copper content in pennies for where this doesnt apply because its illegal to melt down.
Its all just a description of how the market (meaning people ) behaves once the government applies pressure in certain directions.