The point is that the Mint has a large business of selling actual physical silver, not just investment bullion but coins, medallions etc. Which I suspect is their main business. To process the silver can take a significant period of time from buying it to selling the manufactured form. The Mint can try to reduce this as much as possible but the inventory can still tie up large amounts of money which they would have to supply.
By selling unallocated silver, the Mint can use the silver as inventory. It is unallocated but still backed by silver in their own inventory.
However this would only work if unallocated precious metal is a small part of the business, and the Mint was in fact careful to buy 1 oz of actual silver for every 1 oz of unallocated silver sold at the same time as it was sold.
So, no matter how much the price changes the Mint would still hold sufficent metal to pay out the unallocated buyers.
