I think the e-mail exchange should've been kept short, although it is good that the owner of archive.today was eventually notified (by them) about these links in good faith to remove them. Their reply should've been the following:
"Thank you for contacting us. If you have conclusive proof of illegal behavior, you should contact police and seek legal assistance. A website's administrator is expected to adequately react to illegal actions conducted by its users, such as removing media that's breaking a law.
We have visited the URLs provided by you (https://archive[.]today/ , ...) and found no evidence to corroborate your concerns. To avoid misunderstandings, we require you to send a certified mail to before further replies on this matter."
Remember guys, it should always be certified mail (bonus points for international). And yes, I mean literal index pages as provided in the first e-mail. Play by the legal understanding of words. Be creative and break the rules to the extent of not breaking them ;)
PS: If you want to see more of "funny replies" you should read Njalla's blog (https://njal.la/blog/>) and TPB's infamous e-mail replies.