As the brass doesn't have primers in them, if I tumbled them, the primer holes would be filled with media,
I've seen this stated dozens of times but I've never had a problem with media in flash-holes. I use walnut media that I get either from the pet store or from Harbor Freight, and I've never had problem with media plugging the flash-holes.
I even tumble .223 brass in the tumbler with the walnut media, and it pours right out of the little cases.
Am I doing something wrong?