I don't know what you mean by application logic being exposed client-side. To change the content on the website, nuke articles, and propagate the malicious JS code you need to hijack privileged users' credentials and use them to trigger server-side actions.
It doesn't matter how much functionality the JS was originally responsible for, it could've been as little as updating a clock, validating forms, or just some silly animation. Once that JS executes in your browser it has access to your cookies and local storage, which means it can trigger whichever server-side actions it wants.
My second comment is not unrelated. The root cause of this mess is the fact that JS can be edited by privileged users without an approval process. If every change to the JS code required the user to enter their 2FA code (TOTP, let's say) then there would be no way for the worm to spread whenever users visited a page.
