A little research on the Canadian Ballon shootdown a number of years back show that isn't exactly the case. A larger balloon was shot with a (20mm I believe) cannon and continued to float a long distance.
‘Duds’ is an odd way of putting it. Sidewinders usually have an ‘exploding ring of metal rod’ warhead, I believe - and that was replaced by something else better suited to destroying the balloon while leaving the payload intact enough for technical analysis.