1876-P Seated Half Dollar With "C" In Neck — But Doesn't Look Like A Proof?

This is an 1876-P Seated Liberty half dollar variety that shows the upper serif and loop of a "C" in Liberty's neck. I posted a couple of close-ups of the neck, along with a photo from a book that shows this specific variety. There's virtually no question that it is the "C" in neck variety, as the photos are virtually identical and both "C"s are located in the same spot on the neck.

The problem is that the variety is supposed to be exclusive to 1876 proofs -- but this coin is graded "Genuine Cleaned AU Detail" from PCGS (as most of you know, PCGS will note "Proof" on the holder, even on detail graded coins.)

One explanation: PCGS is somewhat notorious for missing proofs during the grading process. I have several Morgan dollars I've cherry-picked over the years that were graded "MS ..." by PCGS, but that appeared on close inspection to be proofs. And sure enough, when I sent them to PCGS to be re-graded, all but one came back as "PR ..."

But this coin also doesn't have that classic "proof" look -- even when accounting for all the wear and chatter. I admit, though, that distinguishing between business and proof strikes can be difficult, depending on the series, when there is even a modest amount of wear and/or chatter. Also, I should point out that I am definitely NOT an expert -- or anything close -- when it comes to Seated halves.

SO ... my question is, do I have a proof half dollar here? Can it be anything else, given that it has the "C"? Could it be a business strike struck on a proof die (though wouldn't that still come off looking like a proof? I'm not sure.)

Thanks for any help you can provide!