Hiya … did you get a chance to look at this? … I've got artwork piling up waiting to go to print, and more and more related problems stacking up as I examine each file and discover the next weirdity (for example, I've got a different job with 6 black logos overprinting a coloured photo. All overprint except one, which is knocking out … but nothing obvious to suggest why!(?).
Sorry for answering so late.
So far the display in the Attributes panel is normal. When there is no fill on the object, there is a strikethrough.
In your situation this is getting so difficult to check, because your black is a muddy black. It's been set up in RGB. Same goes for the color objects. So usually for check the overprint you could just turn off the black (or other single inks) in the Separations panel and you know whether it will overprint. Overprinting objects that have more than one single ink applied is usually problematic (which might be why you are asking about this in the first place). Could it be that the artwork originated in a CAD application? Because that would somewhat explain the swatches setup in RGB.
I'm not fully updated about issues in Acrobat. So there may be some warnings in Acrobat that just appear without a reason and I would recommend that you ask about them in the Acrobat forum.
In Illustrator you could use the Astute Graphics plugin InkQuest. It offers an Overprint preview that highlights overprinting objects:
You could also use the free plugin Select Menu to select just the strokes objects and just the filled objects and then check the overprint separately:
AdChoices