Why does area below threshold give an integrated density value?

I took a grayscale stack and made a copy. I used a threshold algorithm to make the copy binary and I also have the threshold active on the image (desired pixels are red). Now I want to measure the grayscale values in the original stack, limiting to the thresholded area of the binary stack. I have both stacks open and 'Limit to threshhold" is checked in Analysis > Set Measurements, as is “Redirect” to the grayscale image.

I get a bunch of data from my ROIs for each slice (#1), but if I make a similar ROI (#2) in the black background (below threshold) it seems to be taking data from the grayscale image anyway because I get numbers in the data table. But I expect this value to be zero and so it’s not doing what I really want. Can anyone explain?

I’ll cite my answer to a different post from 2015 here:

Hope that helps.