I am curious about the "great depreciat(ion)" mentioned in the article. Could this be a reference to the Mint Act of 1857, which caused foreign coins to cease to be Legal Tender in the United States?

I agree with Tom's speculation that this must have referred to the end of legal tender status for foreign coins in 1857. At that point they would have been worth only their bullion value. Since the coins undoubtedly continued to circulate for some years afterward, they would have become a problem to merchants, who would have been loathe to refuse them at the cost of losing a sale.

Banks would not accept them for deposit at their former value, and the merchants would have no recourse but to sell them at a discount to bullion brokers. The same scenario played out again two decades later with the United States trade dollar, which lost its domestic legal tender status in 1876 at the same time as the price of silver was declining.

As for the individual who hoped to redeem his Polhemus-counterstamped pieces for their former legal value, his was a hopeless cause. Polhemus was not endorsing the coins' value in any way; he was simply using them as an advertising medium, and any court would have recognized that fact.