I doubt they actually want people to stop sharing their content on Mastodon, as they share the content on Mastodon themselves. I think they want to get more attention for this issue.

Nobody seems to have done so, but it'd be trivial to use ActivityPub as an amplification factor for attacking small publications. Just register free accounts with a couple hundred servers, post links to articles (with unique garbage added to the end of the URL to bust basic server side caching), and tag a couple dozen random users from other servers. Every server, as well as every server whose user was tagged, will fetch the page, and if present, a header image. You can easily send out dozens of links per second to thousands of servers, enough to overwhelm any site that doesn't have their content gatekept by internet giants like Cloudflare.

If the website is hosted on a server with expensive egress fees ("serverless", Amazon, GCloud, Azure, hosters that don't disconnect your server when you hit your bandwidth limit) you can run up a bill of tens of thousands. If the hoster does apply an egress cap, you can shut down a website for a couple of days at the very least.

I don't have a workable solution to this problem, but the way the Fediverse seems to be built with the rather naïve idea that every request that passes the signature requirement is done in good faith has major implications on the wider internet. If we don't find a solution to this problem, I expect websites to start blocking Fediverse user agents when the first DDoS waves start.