Yes, this is wrong. The pre-World War I classic gold standard was destroyed. No country ever returned to it. The gold exchange standard of the interwar period was pegged exchange rate system in which each country pegged its exchange rate to the pound. the pound was no longer redeemable for gold coin, but only for bullion bars. Thus, it was effectively no longer redeemable for gold for the average person. Look at Part 4 in Rothbard’s book, A History of Money and Banking in the United States:
It is true that after FDR devalued the dollar from $20.67 an ounce to $35 an ounce, that gold, which remained redeemable in the U.S. for foreigners, began to flow into the U.S. At the time, it was called the “golden avalanche.” But this steady, significant gold inflow began in 1934, too late to explain the downturn of the Great Depression which occurred from 1929-1933.