If an image is registered properly, then statutory damages generally applies but that assumes it will be litigated which is costly and risky proposition for the plaintiff. The minimum amount for statutory damages ranges from $750 plus any legal fees.
Judges have LOTS of discretion. I have seen many cases where the party might have won on paper but they ultimately lost because the judge didn't give the plaintiffs everything they wanted.
Whether you infringed "innocently" or "willfully" does matter as a practical matter. It matters in determining the dollar amount. There are lawyers that want to use the legal definition of what "innocence" and "willful" are. But as a practical matter, judges are human beings and many are quite familiar with copyright extortion schemes. The plaintiff might win, but the judge also has the discretion to give (and do) the absolute minimum.
The trouble with too many victims is they are trying to "outlawyer" and "convince" the other side. You will never stun or argue them into silence or submission. They will always have a counter-argument. Some are just plain bimbos. I won't name any names but there are bouncy bimbos in the business.
Most victims will never succeed in trying to outargue them. At some point, victims need to make a very firm, strong stand along with a strong message that there will be an unpleasant and unhappy experience coming after you. (I have a knack for boomeranging on attackers. I can never promise I will win every fight but I can promise to make the experience very unpleasant to unreasonable or irrational people. There are many LEGAL strategies and tactics which are generally beyond the scope of this forum. But just know that they do exist.)
Alternatively, you can hire someone to make a stand for you like Oscar.
I've read that an "innocent infringement" defense isn't possible if the image happens to be properly copyrighted. Is that just a hard and fast rule? Seems like a very easy way for the troll to guarantee a minimum of $750 income off their trolling system no matter what. No?
Also it seems kind of disingenuous, as an innocent infringer obviously wouldn't have had any idea the image was copyrighted one way or another!