The difference is that search engines will generally redirect to the external website while archive.org lets you browse the page on their domain.
As an added exercise, maybe try translate.google.com to see if it's blocked as well.
I'm sure they mean the thumbnail images you can browse in Google's domain.
If this is their reasoning, then it's silly to me. With this logic every search engine should be blocked! Even with all their domain blacklisting simply searching for adult content on google images will yield millions of results. Probably more than archive.org :)
I think this is an honest mistake. I reckon they either had a crawler that flagged archive.org or maybe someone added it by mistake and never realized it :)