Fisher's comment relates to what would happen to the Fed's securities portfolio should there be a sudden or gradual revaluation in the price of gold. His conclusion is that in order to keep the Fed's balance sheet stable, an (acknowledged) surge in the price of gold would lead to a forced selling in Treasurys. Of course, that would mean that the Fed would have to actually value gold at its actual market price, instead of that relic price of $42.22 per ounce. Which means that valuing gold at fair market value would result in dumping over $300 billion in Treasurys, something the Fed can not afford to do at a time when it is engaged in purchasing $100+ billion each month.
Fisher explained that U.S. gold belongs to the Treasury. However, the Treasury had issued gold certificates to the Reserve Banks, and so gold (by these means) also appears on the Federal Reserve balance sheet. If there were to be a revaluation of gold, the certificates would also be revalued upwards; however [to prevent the Fed's balance sheet from expanding] this would lead to sales of government securities. So the net benefit to Treasury would need to be carefully calculated, since sales of government securities would expand the public portfolio of government securities and hence also expand the Treasury's debt servicing burden.