I am going to make some points about the actual topic of this thread, which was Hunter Lead Changes.
Granted, I have been Eventing and also doing Hunters and Jumper my whole life. I have done Dressage independently as well and schooled up 4th Level.
Hunter changes are different than Dressage changes. However, they are only different in the idea that what the original statement or article originally said. Hunters are wanted to be viewed performing a change at a steady gait, flat type of canter. The type of canter that they want to see the horse keep around the entire course. A steady, flat type of canter that shows the horse is obedient, observant, but also enjoying his work. The change is not like one you would see performed in a Dressage arena, where you should be able to notice the horse rocking back on their haunches and noticeably swapping leads.
Now, as far as the rider asking for the lead, they should still ask. It is no different than asking for a change of lead in any other aspect. The rider should never allow on the horse solely, a cue should always be given and the rider should take responsibility. However, there are quite a lot of very well schooled and seasoned hunter horses that will do it automatically, before you can even ask them. They have either done it enough times to know the task by now, or they have been schooled a lot. Hunter horses typically are not taught to counter canter because you want them to learn that when you change direction, you change lead. The idea is that you don't want them to learn that they can counter canter.
I always teach my horses to change lead, and I not once rely on them to just "know". True, there are many spoiled kids and rotten riders in the Rated shows of Hunters that have everything handed to them and then in turn blame it on the horse when something is messed up. But I think we can all agree that that is not the proper fashion, in any discipline. One should have more self dignity than that. And I can safely assume that there are plenty of riders out there, like me, who actually do the work & sweat and put the time into our horses, and do it correctly.
With that said, let me address one more point. I can speak for myself when I say that I always incorporate Dressage into all of my Hunters. When asking for the change of lead, it is always neccesary to make sure the horse is using their hind end to support themselves. Although Hunters do like the 'flat changes', that does not mean a horse can "run" on their forehand into the change. A horse still needs to be using their hind to propel themselves. Therefore, when starting the process with a young/green horse, I always incorporate dressage in their training. I always incorporate dressage into their training regardless.
That is my .02 cents.