Integrity is not guaranteed but could be
Hash of the page made (with a decent hashing standard to avoid collisions) as soon as it's mirrored and that hash stored in a blockchain or another tamper proof method, then it can be trusted a lot more.
All it takes is for one vulnerability or a determined hacker to phish their way in to their systems and modify some content and the trust is all gone. It's no good saying the files or disk is read only when someone can change the links and results to point to their own created content instead.
Archive.org is far from perfect as evidence as it stands imo. It could be made better for evidence integrity but as long as they continue to do the great job they started out to do, that should be their main focus.