"Limit to Threshold" Behavior


I am attempting to select only foreground thresholded (white) pixels on a duplicate image that was thresholded via Auto Threshold, and measure those pixels on the original image. I have noticed that when selecting pixels with the wand tool, that black pixels are included in the selection if completely encompassed by white pixels. To get around this issue, I selected the Limit to Threshold option in the Set Measurements menu. Oddly, the measurement is not limited to thresholded pixels when redirected to the original image, and rather is only limited to thresholded pixels when not redirected (evident by area and integrated density in results table).

I was wondering if this was intended behavior, and or if there is any way to only select/measure foreground pixels exclusively, even when they encompass black background pixels.