I am sorry that details escape my memory at this point, but I have seen a couple instances recently where journalists tried to archive news stories and were served a response that someone has barred articles from this site from being archived. There is also no guarantee that something once archived there will not be removed when they are put under pressure or terms of service change.
So at one point the answer was robots.txt and now it's not: https://blog.archive.org/2017/04/17/robots-txt-meant-for-sea... - that information appears to be current - email info@archive.org and request removal is the process, which some "reputation management" firms talk about. Weirdly I can't find much info.
Furthermore, I don't think archive.org tries to hide/obfuscate their user agent so it's relatively easy to block them - I know that it's possible to manually upload stuff to archive.org, and there are other sources (partnerships with Cloudflare and Brave, at a minimum) but that's not as easy as the Wayback Machine.
I haven't heard anything about this, could you elaborate or link to some article?