I suppose “evidence that the site’s leadership has permanently changed” would convince me. Whoever decided to put in the code that causes visitors to DDOS someone should never be running a web site again.
So, in your mind, there is no way for an individual owning archive.today to recover from this?
I mean, probably not. Maybe if they posted a public apology (an actual one, not a 'I'm sorry I was caught' one), listed the steps that they would take to ensure it doesn't happen again and how the fact that they weren't doing it could be publicly verified.
They've shown they're willing to deliberately weaponize their users to fight a personal dispute with someone, and didn't take corrective action when called out. Trustworthiness is something you lose and don't get back.