The user helps free the Internet by using archive.is as an openly accessible backup platform.

dude... haha it's a random person on the internet who is doing it for free.

They (archive.is) would have built the extension to send the current page content to their servers and the user would have installed it so they can archive internet pages. https://help.archive.org/help/save-pages-in-the-wayback-mach... (item 2)

I suspect most content publishers would go to the source. If there are people who are already willing to pay for subscriptions and ignore the terms of those subscriptions, it's not much of a stretch that they'll ignore the fact that they got their subscription cancelled once (or twice, or however many times). The publisher would more likely see results taking legal action against the archivist.