Browsers copy and store websites as part of their normal functioning. If you didn't want your website to be copied and stored then maybe it was better not to put it up in the first place? Anyway the IA will remove everything with a very simple, automated text file placed in the root directory.
They are saying that your overly theoretic application of copyright is in absolute contrast to the technical realities of how the web works.
It's a discussion that's been had for literally decades, because most tech-fluent people realized a long time ago how a copyright that's designed for physical distribution does not lend itself well to the intangible nature of the web, were replication is trivial and in many cases a mandatory necessity to enable a lot of functions in the very first place.
Sadly that discussion simply died out at some point, I think it was around 2010 when smartphones and social media started to boom, so the copyright reform that was supposed to "fix" all this never came.
Where did I say that? By putting up the website you did, however, give implied permission to use it in ways which are fundamental to how the web works, otherwise why did you put the website up?