The process of refining and purifying silver and gold yields a product that is improved over the pre-treated metal. The sons of Levi might already have the priesthood to offer sacrifices to the Lord, but that priesthood will become more pure, more powerful. In the context of a betimes wayward Israel, this is also a metaphorical atonement, where the priests who had continued to act in their office while in a state of departure from the ways of God are cleansed so that their offerings are again done “in righteousness.”
In the Bountiful context, there is no known history of the cultural departure from the ways of God for the religious hierarchy. The entire religious structure in the New World developed differently from that of the Old, and it is not known how the priests who officiated were related to the gospel and the government. One would suppose that while the church was in the majority, the government and the priesthood that offered public sacrifice would have been righteous. In more recent years there was opportunity for a separate and unrighteous priesthood as the church became a minority in the land.
In any case, this was a text from the brass plates, and the people in Bountiful would find in it the points of congruence, and easily pass over those parts that were not as applicable to their particular situation.