I had read that modern stone washing is done with rough-surfaced ceramic beads. I don't see any reason why actual stones wouldn't work, but what's the difference in finish quality using real stones, no two of which are ever perfectly identical?
Here's the short list of barrel tumbling media:
Walnut shells - nice for softer metals like aluminum or brass
Silicon Carbide grit & Aluminum Oxide grit - used on harder metals (> 40 HRc). Fast deburring & edge rounding
Stainless Steel shapes - very aggressive because of density
Carbon Steel shapes - less aggressive than stainless, less costly for some parts
Ceramic Preformed shapes - wide variety of sizes, shapes, grits, etc. Used for many applications
Order up a sample of each one in each grit & each shape and you'll have hundreds to test
Real stones likely were used early on & there are historical references dating back to 1890. The biggest advantage to purchasing media from a specialty supply house is the consistency. Another benefit is tech support as this is a highly variable process & not everything goes as planned.