NOT TRUE unless you get foolish about enlarging the flash holes. Ever since I purchased my Thumblers Tumbler with stainless steel pins I've been reaming the flash holes in my cases to 0.083 inch to insure that I don't get a case with 2 pins stuck in the flash holes. Learned that lesson with the first batch of 38 special cases I cleaned in the then new Tumbler, had to poke stuck pins from at least 10 cases.
Recently I picked up 1000 once fired Lake City 223 cases and because my initial batch didn't seem to need that reaming operation I skipped it. Turned out that I was wrong about that. After priming 300 cases I got a bit paranoid about not reaming that brass so put all 300 cases in trays and checked them on a small light box I used to use for sorting slides. Found 3 cases that had 2 pins stuck side by side in the flash holes. That probably would have produced a squib if I had loaded those cases and tried to fire them.
As a result I now ream ALL of my brass, even the Lake City brass of which only about 5% actually needed reaming. I've also learned that there is a LOT of variation in the size of Flash Holes, probably as much as 0.006 or 0.007 inch. Generally Remington, Federal LP, and Starline cases run larger with flash holes quite close to that 0.083 ream and Winchester, Speer, and Federal SP cases having flash holes where you can feel the ream working. BTW, I found that genuine Latex gloves help provide me with enough "traction" to keep the cases from spinning in my fingers when I insert the drill with the ream. Yeah, I do this by hand and yeah, it is a bit of a PITA. Fortunately I only have to do it once.
PS: 0.083 diameter reams can be purchased from Production Tool or MSC Industrial Supply and the Cobalt reams are not cheap at about 20 bucks. They are also way long and I would suggest using a Dremel to cut the shank length down to make them more manageable in a hand drill. Good news is that after many many thousands of cases my ream is still sharp and cutting consitently sized flash holes.