Note based on some very helpful emails about this from the people that wrote the articles cited above, and the discussion above, the right answer seems to be: do not try to "fix" individual points in an ROC curve unless you build an entirely new classifier, and then be sure to leave out some test data to see if that was a reasonable thing to do.
Getting points below the identity line is something that simply happens. It's like getting an individual classifier that scores 45% correct even though the optimal theoretical minimum is 50%. That's just part of the variability with real data sets, and unless it is significantly less than expected based on chance, it isn't something you should worry too much about. E.g., if your classifier gets 20% correct, then clearly something is amiss and you might look into the specific reasons and fix your classifier.