They can also choose not to include stuff in their archives, sometimes in ways that assist folks who've been spreading misinformation. For example, they've manually excluded all Snopes' content from the archive, effectively helping them memory-hole old versons of their fact checks. I discovered this after Snopes falsely claimed that an EPA rule tightening asbestos restrictions in the US was actually allowing prevoiusly-banned uses to be approved for sale and convinced a bunch of HN readers of this. A month or so later, the EPA pointed out that the very document Snopes had linked said that only uses which were previously not restricted at all could be approved for use and that the previously banned uses remained unconditionally banned.
Rather than correct their error, Snopes deleted the part of the article which claimed the ban was being removed, pretended they'd never said that, kept their original now-unfounded conclusion, and wrote a blog post accusing the EPA of lying for claiming that they'd made an error in the first place. Good luck finding the original article with the error online now. (There should be a copy on archive.is, but they're having uptime issues now.) The Internet Archive basically helped one of the trusted sources we're meant to rely on to spot misinformation rewrite the past to gaslight the US government.
The Internet Archive also took the decision not to allow government websites to block content from being archived or removed around about the time Trump took office. So they're very selective about who gets to hide their past errors like this and whose pasts are permanent public record for all to see.