The solids talked about are not something you can filter out with cheesecloth.
Example-
Lane oil contains solids (ex- one brunswick oil has 100% solids in it.) like the UV additive is a solid in lane oil and is measured in parts per thousand (USBC equipment specs says 1 part per 3000 of the solid content). "Solid Content" here means the lubricants remaining after subtracting all solvents and volitiles.
so if you pour oil thru your cheesecloth you wont find a bunch of grit like particules filtered out.
The elixir is similar to that in that it can have a solid content. But you wont find it filtering that way.
Im sure some else could explain this better.