After reading the Venerable's book and also reading other writings he has done, I don't think what he is talking about is going against their (Joseph G and Bhante G) actual way of practicing. Thanissaro critiques the way they express what mindfulness is, or maybe their definition of mindfulness, but when looking at how Thanissaro defines mindfulness and others (alertness and ardency) it fits into the other "buddhist teacher's" actual practice.
"The term mindfulness means being able to remember, to keep something in mind. In the case of establishing the body as a frame of reference, it means being able to remember where you're supposed to be — with the body — and you don't let yourself forget. The second quality, alertness (sampajañña), means being aware of what is actually going on in the present. Are you with the body? Are you with the breath? Is the breath comfortable? Simply notice what's actually happening in the present moment. We tend to confuse mindfulness with alertness, but actually they are two separate things: mindfulness means being able to remember where you want to keep your awareness; alertness means being aware of what's actually happening. The third quality, ardency (atappa), means two things. One, if you realize that the mind has wandered off, you bring it right back. Immediately. You don't let it wander around, sniffing the flowers. Two, when the mind is with its proper frame of reference, ardency means trying to be as sensitive as possible to what's going on — not just drifting in the present moment, but really trying to penetrate more and more into the subtle details of what's actually happening with the breath or the mind."
Bhante G in mindulness in plain english:
"In spite of your concerted effort to keep the mind on your breathing, the mind may wander away. It may go to past experiences and suddenly you may find yourself remembering places you've visited, people you met, friends not seen for a long time, a book you read long ago, the taste of food you ate yesterday, and so on. As soon as you notice that your mind is no longer on your breath, mindfully bring it back to it and anchor it there."
There is not much going on differently there between the two Bhikkhus practice.
I know Joey G practices Mahasi style (like myself)... So again lets first look at Thanissaro:
"Just be with the body in and of itself, sitting right here. You close your eyes — what do you have? There's the sensation of "bodiness" that you're sitting with. That's your frame of reference. Try to stay with it. Keep bringing the mind back to this sense of the body until it gets the message and begins to settle down. In the beginning of the practice you find the mind going out to grasp this or that, so you note it enough to tell it to let go, return to the body, and hold on there. Then it goes out to grasp something else, so you tell it to let go, come back, and latch onto the body again. Eventually, though, you reach a point where you can actually grasp hold of the breath and you don't let go, okay? You keep holding onto it. From that point on, whatever else that happens to come into your awareness is like something coming up and brushing the back of your hand. You don't have to note it. You stay with the body as your basic frame of reference. Other things come and go, you're aware of them, but you don't drop the breath and go grasping after them. This is when you really have established the body as a solid frame of reference."
I've heard Joey G guide a meditation almost the exact same way. At times JG uses sound or the breath instead of just the body, but other then that; nothing different.
So from what I gather from the book, his main issue is the way certain teachers define mindfulness.. Because I have never heard either Joey G or Bhante G say "just let your mind wander freely"
"whatever one frequently thinks and ponders upon will be the inclination of one's mind"