Bullshit!!!! Been wet tumbling with steel pins for years without issue. 223 rem, 6.5 creed, 6 creed, three 6 gts, 22 gt, 25 gt, 7/300 prc, 6.5 prc, 338 edge, 338 lm. Never an issue.
You may not be seeing it - and if so, good for you. You only have to Google "wet tumble peening case mouths" to find threads here and on a number of other forums. In my friend's case, he stopped wet tumbling, and the problem stopped immediately. The only thing he changed was tumble method. Might have something to do with size of the pins, or time he was tumbling, or the tumbler in use, etc. Even dry tumbling can peen the cases mouths, but it takes a lot longer - wet tumbling involves the cases falling on one another, typically, where they just bump into one another in dry media.