I've tumbled brass with primers in them, lots of times. Never saw a failure...
Maybe ignorant is bliss..... who knows.. but I'm sure someone will be along to tell us.
With the usual campfire slander included, of course!.
I've seen guys do this and then wonder why they are getting misfires. One guy asked me why his primers were bad, I had him go over his reloading steps, and sure enough, he had tumbled primed brass for some reason. I told him to stop doing that, change his process, and sure enough, his bad primers turned into good primers, once he stopped doing this..
I know for a fact that when I tumble brass, I always have to poke small granules out of the flash hole, before I prime them. Guys do some weird things, and we all have our own way, but I won't tumble primed brass for any reason. Like I said before, deprime and then tumble.. problem solved. Hey, you can even use those primers that you took out of that brass too.