You'd think, but then you get into the "What is the real definition of a 'trigger'?"Wouldn't the main point be "one shot per single function of the trigger"?
That's why there is substantial ambiguity when it comes to what would seem to be a clear cut case of the trigger being repeatedly operated.Since you pull on the ring and not the trigger, the ring becomes the new "trigger" and the trigger itself becomes sort of an auxiliary sear.
Thus, in the ATF's eyes, the trigger you're pulling on is depressed once and the gun keeps running.
Many machine guns work on the same principle, where (usually) the closing bolt trips an auto-sear which drops the hammer again. The shoestring just brings the action to the outside of the gun.