Well, the site would have to react to any DMCA takedown notices immediately, but wouldn't be liable for any infringement (so-called "safe harbor" rule).
But you ask a very good question with regards to the spread from there. I suppose, as long as you complied with an cease-and-desist orders, you'd be demonstrating a good-faith ... aaah, I'm just throwing words at a screen now. I'm not a lawyer. The law is often arbitrary and confusing from my perspective.
You're apparently assuming the sites are all hosted in USA, not an entirely terrible assumption. [Though there is a similar Electronic Commerce Directive in Europe and probably other similar laws in other jurisdictions]
As I understand it DMCA Safe Harbour is for sites where they transmit media without interaction, users upload but the site is there to simply serve the media. If the site were selling the media (direct financial benefit) or offering a commercial license for it then Safe Harbour doesn't seem valid? Applying a license would possibly be considered transformative? Similarly if the site is selecting the images to meet their requirements - using a [partially] manual method then it seems DMCA Safe Harbour wouldn't cover it.
But you ask a very good question with regards to the spread from there. I suppose, as long as you complied with an cease-and-desist orders, you'd be demonstrating a good-faith ... aaah, I'm just throwing words at a screen now. I'm not a lawyer. The law is often arbitrary and confusing from my perspective.
Caveat emptor seems to always be on order.