AJAX in the ACP Does not work wherever Confirm Box modals are used

Any AJAXified buttons in the ACP that present the confirm box modals do not work.

The AJAXed Run Now buttons in the "Resynchronise or reset statistics" block on the front page of the ACP do not work. The AJAX script (core.js) is not running the correct PHP. So confirming to Purge the Cache, for example, does nothing.

Trying to delete custom BBcodes does not work.

Trying to delete Modules in Module Management does not work.

Etc.. Etc.. for wherever an AJAX confirm dialog comes up in the ACP.