Ideally, burnishing is a non-abrasive process; i.e., it does not remove material. In practice, depending on a variety of factors, some material is likely removed. After all, there are instruments that can detect the removal of a single atom (for particular materials under particular circumstances). Here, I consider burnishing to be a non-abrasive process on the macroscopic level. If I sharpen a knife edge with an abrasive whetstone, metal particles are readily visible on the whetstone (as long as the whetstone is not black) and on a white (or other light-colored) paper towel or cloth used to wipe the knife edge. But if I burnish a knife edge with a non-abrasive burnishing rod, generally no metal particles are readily visible on a white (or other light-colored) paper towel or cloth used to wipe the knife edge or the burnishing rod. If the knife edge is nicked, however, then burnishing can cause stray chips of metal to break off from the damaged nicked regions.
Two key factors are required for burnishing to be successful: (1) The material of the workpiece (the object being burnished) must plastically deform when the burnishing rod (object doing the burnishing) is applied to the workpiece. (2) The material of the burnishing rod must be harder than the material of the workpiece.
In our instance, the workpiece is a blade (knife blade or figure skate blade). If the blade material is too brittle, the edge will likely chip, rather than plastically deform, when a burnishing rod is applied to it. This is an issue with some knife blades, but not with figure skate blades, since figure skate blades must withstand the impact of stroking, jumps, and landings.
Commercial burnishing rods are used in woodworking to form the edges of card scrapers. They are also used in the fabrication and repair of music instruments. Most commercial burnishing rods are made from tool steel, but at least one is made from tungsten carbide. The steel in some knife blades may be harder than the steel in some burnishing rods. But tungsten carbide is harder than any steel used for knife blades or figure skate blades.