The only reason you shouldn't tumble loaded brass is that "everyone on the Internet says no!"
I've tumbled it for years and haven't had any sudden explosions, broken rifles, etc. Some have even heard this admonishment so long they've run their own tests. Tumbled loaded ammo for 24 hours or more, disassembled it, and examined powder for any signs of breakdown, powdering, etc.
It's am matter of choice but a 10 minute trip through the vibrator in corncob will take all the lube off with no damage.
You can believe those who are merely parroting what they heard or read on the net or you can believe those that have done it for years (over 30 for me) without incident.
Give it some thought. Did all those GI's in Vietnam, Iraq, Afghanistan, receive ammo that WASN"T subjected to hours and hours of vibration? From the plane that took it to the country, the C-130 that took it to the Bases, and the helicopters that then transported it to the FOB's, there was more vibration and rough handling of that ammo than if you left it in your "tumbler" filled with ground corn cob for a week. Hell, even if it wasn't transported to an FOB by chopper, ever rode in the back of a military truck?