Do AI image detectors still work on screenshots and reposted images?

What I have noticed over the last few weeks:

• The same image gave "likely AI" from one detector and "likely real" from another, both on a repost.
• A screenshot of an image I knew was a photograph came back flagged on one tool. I only knew it was a photograph because the photographer had posted the original.
• When I could find a higher resolution copy, the results were steadier, but that is exactly the case where I need the detector least, because I can usually trace the source.

My current working rule is that a detector score on a repost is a note in the file, not a reason to share or not share. If I cannot find the earliest copy or a credential, we do not post, and I would rather skip a viral image than guess.

What I would like to understand:

1. Why do screenshots and reposts hurt detector results? Is it compression, resizing, or something else?
2. Is there any check that survives a screenshot, or is that the point where everything is lost?
3. If I can only get the repost, what is the most defensible thing to write in our internal log?

I am a cautious person by temperament, so please tell me if I am being too cautious.