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Well, let's do a quick survey to test your theory.
Of the threads in this forum that have new posts in the last two days, here's the tally of the attacks mentioned in originating posts. This is only a tally for those posts in which a specific attack was mentioned in the OP, and I could tell whether the birds were penned or not. Oh, and I had to estimate on the deaths while penned for one attack, because the lady who posted about the most recent bear attack never clearly identified how many hens were killed (she specified three ducks, but didn't specify on the chickens).
attack incidents while free-ranging: 8
attack incidents while penned: 3
deaths while free-ranging: 15
deaths while penned: 10
So far, your theory doesn't seem to hold water. Also, remember that many people who have predator losses while free ranging won't bother to post about it -- as other people have already mentioned, they EXPECT losses so it's probably nothing worth bringing up in most cases.
I think your sampling protocol is faulty.