They're saying that *everything else being equal* a strikeout doesn't cost more than about .02 runs. Supposing you had two players who both batted .250 and hit 18 homers, then the one who fanned 60 times and popped up 20 times didn't gain you anything over the one who fanned 80 times.
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Infield pops have a value of (let's just say) -.25 runs to the scoreboard while strikeouts have (let's say) -.26 runs. Groundball outs have (let's say) -.20 runs after you factor in advancing runners, GIDP's, etc. It's only in that sense that a strikeout doesn't hurt the batter.
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But of course putting the ball in play gives you a 25-35% chance for a hit, so strikeouts often drive batting average down ... unless the hitter is gaining BIP velocity and therefore BABIP gains.
Don't remember the methodology but James said *for a pitcher* a strikeout means gains, while for a hitter it's no loss -- ergo the steady rise in K's. Probably since a pitcher is gaining no BIP advantage by throwing for contact rather than missed bats.
Don't know if that answered the Q?