en.wikipedia.org/wiki/Miscibility

In materials science, an alloy is a metallic material made from two or more elements; it does not have to be a single-phase, fully miscible solid solution. U.S. Department of Energy material explains that “metal alloys are materials that contain two or more atomic metal elements.” A separate OSTI-hosted research paper explicitly discusses “immiscible metal alloy systems” and “Cu-Ta immiscible alloy thin films,” showing that metals can be immiscible and still form alloys. The usual consequence of immiscibility is phase separation or a heterogeneous microstructure, not the impossibility of alloy formation.

This sentence overstates the behavior of silver in molten lead. The NIST Ag–Pb phase-diagram page lists a single liquid phase, shown as L with model (Ag,Pb), which is the standard notation for a liquid solution of silver and lead rather than two immiscible liquids. In other words, molten silver and molten lead are liquid-miscible.

A National Library of Medicine / NCBI reference on lead refining describes the Parkes process differently: precious metals are removed because they are more soluble in zinc than in lead. That only makes sense if silver is already soluble in molten lead bullion. So the clause saying silver is not miscible in liquid lead is incorrect.

In the industrial Parkes process, removing zinc from the silver-rich crust does not directly leave “nearly pure silver.” A U.S. Department of Energy mining profile explains that after retorting, the remaining retort metal contains silver, gold, copper, and lead and is sent to a cupel furnace for additional refining. Only after cupellation is a silver/gold alloy (doré) produced.

The NCBI Bookshelf description of primary lead refining is consistent with this: Parkes removes silver and gold by transferring them into zinc, and later steps are still required to remove zinc and other remaining impurities. So the article skips important refining stages and describes the intermediate product as much purer than it actually is.