I disagree and will demonstrate. I know of several establishments where if I take a dollar’s worth of pre-1965 coins I can spend them at today’s silver rate based upon their content. The operating logic is that the “dollar” I am spending, call it an AG-dollar is directly related to silver. Gresham’s law actually proves my point. So long as the government issues silver alloy coins and agrees to trade one-for-one for the face value of bills (i.e. Ten silver alloy coins for a paper ten spot) the value of US currency will be tied to the market rate of silver. It would immediately increase the purchasing power of the dollar
So what happens if the government prints 10 times the number of paper dollars without a corresponding increase in the amount of silver-containing coins? The same thing that happened in 1965 - the silver-containing coins get yanked out of circulation by ordinary folks as the price of silver rises to the point where the silver content is worth more than the face value of the coin.
I think that what you are saying is that the purchasing power of the silver-containing coin will remain constant - and there I basically agree with you (unless the supply of silver suddenly jumps or declines). However, without the supply of paper currency somehow limited such that the "reserve ratio" of silver to paper remains roughly constant, then the paper dollars will lose value compared to the coins containing silver.