Refining silver and gold yields a product purer than the pretreated metal. The sons of Levi might already have priesthood authority to offer sacrifices to Yahweh, but it will become purer and more powerful. In the context of a sometimes wayward Israel, the metaphor also represents atonement; priests who had continued to act in their office while straying from God’s ways are purified so that their offerings are done “in righteousness.”
We have no record that Nephite religious leaders departed from God’s ways. The New World’s entire religious structure developed differently from that of the Old. We do not know how the priests related to the gospel and the government. Presumably, while believers constituted a majority, the government and the officiating priesthood would have been righteous. More recent years when believers were a minority might have allowed a separate, unrighteous priesthood associated with the majority.