Good question. Here's my thoughts on the issue:
1) Generally speaking: No, I would not agree that Buddhism is anti-thinking. Is Buddhism against attachment to thinking? I would say yes. But Buddhism is about going beyond attachment to everything, not just thinking.
Right View (or at least, "Right Conceptualization"...if there is such a thing) requires us to hear the Dhamma, to remember it, to consider it for ourselves, to apply what we have learnt and to reflect on our experience. Concepts such as "Four Noble Truths", "Noble Eightfold Path", "Three Characteristics", etc. are to be seen directly...but before we can see these things directly it is probably going to be very helpful to think about them at least a little bit. Even if we are a so-called "Faith-Follower" we still have to know what exactly we have faith in. How can we practice the Noble Eightfold Path if we have no conceptual framework to know what it is we are trying to do?
2) Regarding Ajahn Brahm's advice: I cannot speak for Ajahn Brahm and I don't intend to put words in his mouth but I am reasonably familiar with the way he teaches meditation and have been on some of his retreats so I will speak about the way I understand his meditation method. Ajahn Brahm talks a lot about inner-silence because of it is conducive to stillness. The Jhanas, according to Ajahn Brahm, are deep states of stillness which cannot be reached by thought and no thinking can take place within Jhana. So, if this definition of Jhana is accurate, it makes sense that the way leading to such states is (partly) a result of stilling the mind. Ajahn Brahm does teach people to use some thoughts (e.g. counting the breath, mantras) in the early stages of meditation if they are useful in pointing the mind in the direction of stillness. But he teaches that such thoughts are limited in their usefulness and eventually when the mind becomes peaceful enough you can let them go.
3) Regarding my own experience: I am a habitual thinker and, as a result, this can be a hindrance when I meditate. I have only been meditating for about 2 years and I realize that calming the mind and re-training the mind is a gradual process. People who habitually think too much are going to have to learn how to let go if they want to meditate. Thinking too much is just one obstacle, there are many others as well.
Four types of letting go:
1) Giving; expecting nothing back in return
2) Throwing things away
3) Contentment; wanting to be here, not wanting to be anywhere else
4) "Teflon Mind"; having a mind which doesn't accumulate things
- Ajahn Brahm