You can see from the plot that I_shuffled and I are about the same; sometimes I_shuffled is greater than I, sometimes it's less than I, but it never differs by more than 10%.

The reason we didn't use I-I_shuffled in the paper is that there's a potential confound. One can, in principle, get cases where I-I_shuffled=0, but correlations are actually important. This could happen because of cancellation effects (explicit examples can be provided, if you're interested).

The reason we used our measure, Delta I, is that it's an upper bound on information loss. Thus, if Delta I=0, there is an absolute guarantee that one can ignore correlations and recover all the information in the responses.

One last thing ... the fact that the maximum information loss measured by Delta I (11%) was not much more than the maximum value of |I-I_shuffled| (10%) indicates that the cancellation effects we were worried about don't happen in real life. But there was no way to know that until we did the analysis with Delta I.