It's not really a "concern", per se - like I said earlier, I don't think that the amount of metal lost when you remove tarnish/corrosion is significant enough to cause concern.
I just don't think that his solution (one drop of soap and 1/2 - 2/3 teaspoons of citric acid in a quart of water) makes much sense when wet tumbling with stainless pins. If you're just going to soak the brass in a bucket, or use an ultrasonic cleaner, then that's a different story, and more acid/less soap makes sense.
But if you're tumbling with stainless pins, I think it makes more sense to let the mechanical action of the pins do the work, rather than relying on the acid solution.
It's the same thing when I'm polishing brass around the house. If I wanted something that I could just "dip and rinse", I'd use something acidic like Tarn-X. The part will quickly come out clean, but I know that I'm going to end up with slightly pink, somewhat dull brass, like the cases in your second picture. But if I know that there's going to be mechanical action involved as well (like applying the polish with a cloth and then buffing it off), I'd use something less acidic, because I get better results.