If the state of a webpage in the past matters to you, you need a record that won't cease to exist when your opposition asks it to. This is the concept behind perma.cc.
edit: "Other types of removal requests may also be sent to info@archive.org. Please provide as clear an explanation as possible as to what you are requesting be removed for us to better understand your reason for making the request.", https://help.archive.org/help/how-do-i-request-to-remove-som...
If you were photocopying a textbook and giving it to your classmates, the publisher could have their lawyer send you a Cease and Desist letter telling you to stop (or else). But if they told you to burn your copy of the textbook then they would be overreaching, and everyone would laugh at them when you took that story to the papers.
Legal reasoning from made‐up examples is generally a bad idea, but I think you can safely reason from that one.
I’m not privy to the actual communications in these cases, but I suspect that instead of replying back with “we deleted the content from the Archive”, they instead say something anodyne like “the content is no longer available via the Wayback Machine”. Smart lawyers will notice the difference, but then a smart lawyer wouldn’t have expected anything else.
What? That's the only way to do legal reasoning, and as an obvious consequence it's how both lawyers and judges do it.
You are wrong, copyright specifically prohibits copying, not distribution. They can get a cease and desist that requests you destroy property and they ca get a court order backing that which will put you into contempt of court if you fail to do so.
Proving damages is easier with distribution, but that is a civil matter not a criminal matter.
You do realise the "downloading" is implicitly a copy.
If you want to actually have a civil discussion then you need to make some reasonable argument than "They're not making copies either."
Sounds like whatever role you played at IA when you were there didn't give you any actual insight into what happens in operation and you simply tried to prove your point with an appeal to authority instead of backing it with facts and reason.