For me, the statement piece is the one that screams "LOOK AT ME"
My phone case often falls into statement territory, since I'm not much of a pink glitter kind of girl. It totally stands out against my really RATE looks (which is exactly why i chose it LOL)
My h&m trashed sweater winds up being more statement than I ever expected it to be (i mean, really, its just a ribbed burgundy sweater). I get comments on it every single time I wear it in public; apparently, it screams at passers-by
My grey Benenato sweater definitely qualifies as statement, since it looks like it survived battle with a lion in the Roman colosseum.
The navy blue do.ri tank looks like a normal tank top from the front, but it's rather like a mullet haircut (all business in the front party in the back LOL). So I classify it as a statement piece.
As for whether or not you can take the statement out of a statement piece, I think my spider brooch might be a prime example. I'm still waiting on it to arrive, but it seems to have statement potential if worn with something less RATE. It would probably lose all of its impact if I wore it with an all black emo or goth sort of outfit or with any outfit around Halloween.
I get really confused about "statements" sometimes, and a Google search for "statement necklace" just added to the confusion. I cannot for the life of me understand why the first 3 pics are coming up under a search for "statement necklace" because they just look very ladylike to me. The fourth one, well, I guess I can see why it's coming up (big and sparkly) but I feel like big and sparkly isn't enough to qualify as "statement" anymore because we see it in some variation or another so very often. The last pic feels very statement to me, maybe because it's so different from all the rest? And don't get me started on statement shoes, because an image search just brings up a ton of shoes that look overwrought or overdesigned (or child's craft project gone wrong in some cases).
Maybe statement pieces can be oversimplified by defining them as "that's a lot of look"? (No judgement implied with that quote, because my "lot of look" might be your essential and thats perfectly cool)