Just for the sake of clarity, when Purdue University says something like a herbicide is not "registered for use in Jerusalem artichoke" it doesn't mean you can't use the herbicide on a plant. It means that, if you spray it, you can't then harvest and sell it. If they say something like it's 'not registered for the control of such and such plant', that means you can't use it, period. But, you don't see the latter all that often.
One last thing, the willingness of people to go "off-label" is one of the reasons herbicides ought to be much more heavily regulated in this country.