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Mal, your numbers aren't correct, though your thought process seems valid to me. The infield fly ball percentage is not of all the ball in play, but rather only the fly balls in play. So it is 6 pop-ups, 19 outfield flyballs, 39 ground balls, and 26 line drives. Using the average BABIP for the distinct hit types found here, http://www.brewcrewball.com/2008/4/22/447297/all-about-babip, Ichiro would have a BABIP of 0.342. This would give him a BA of 0.323, rather than his current 0.281.
I would also like to point out that Ichiro has used a more agressive approach in the past, in particular in 2005 when he set his personal ISO record, set his career high for homeruns, set a career low for infield hits, and prior to 2011 had his lowest BA of 0.303. Anyway using his batted ball data from 2005 would have 'predicted' a BABIP of 0.322 versus his actual of 0.316. Given that Ichiro gets a high rate of infield hits and therefore has a higher than average BABIP for ground balls, it seems likely he runs a lower than average BABIP for line drives. How much lower, I don't really know.