Rebs there is nothing wrong with trimmer. I would lay a hefty wager on bent, and/or thin weak rims. For .223 Rem I have found AR fired Remington brass to be the worst about doing this. In fact if I see a head stamp of R-P on .223 I scrap it for just such reason. Some others will do this as well I just scrap them due to the fact that I have so much .223 brass anyway.
If your cordless drill has a setting for lower speed try it on the lower speed it helps to prevent some of the wobble effect from badly bent rims.
No matter how many times you do it and nothing happens it only takes something going wrong one time to kill you.