Is it that much better that Archive.today reserves the right to edit old archived pages for the owner whenever they have a petty grudge with someone?

At least site owners have the copyright on the pages that Archive.org saves. They can just get the content pulled through DMCA anyway.

Folks keep saying this

Do you actually mean edit or do you just mean delete

Both are problematic, but falsifying a historic record is orders of magnitude worse than deleting one, and conflating them would be extremely dishonest