Thinking is required in buddhist practise, it's just not thinking about anything you please.
Also, one usually deals with the coarser forms of suffering first, and no special esoteric philosophies and techniques are needed to address them, usually just clear thinking and problem solving is required.
Just before Ninakawa passed away the Zen master Ikkyu visited him. “Shall I lead you on?” Ikkyu asked.
Ninakawa replied: “I came here alone and I go alone. What help could you be to me?”
Ikkyu answered: “If you think you really come and go, that is your delusion. Let me show you the path on which there is no coming and going.”
Your everyday conventional wisdom is not negated by buddhism.
For example, buddhist people use the word 'I' all the time ("Let me show you the path on which there is no coming and going."), despite trying to realise the doctrine of 'no self" in their practise.
The doctrines attempt to eliminate suffering, proceeding from the coarsest levels down to more and more subtle forms of suffering.
The delusion the monk is suffering from here, can only become uncovered after much work has been done clearing the way first.
They are not true and false at the same time, they are only commonly understood to be a contradiction, and the point of the koan or statement is to push the practitioner to is to see through the apparent contradictions.
Koans and Zen stories are a training aid, but are not a substitute for common sense.
Usually the contradiction occurs because the opposing statements come from different levels of analysis (the conventional: "I am going to 7/11 to get a drink.) the ultimate (I am just an unfolding process dependent on conditions that changes from one second to another, so in a way there is no I that goes to 7/11 ...).
The thing is, even though 'ultimate' sounds more awesome, buddhists say "I" all the time. Just the same way that engineers use classical mechanics every day for certain classes of problems, because there's no need to bring in disappearing cats and quantum weirdness for that level of analysis.
To every level of suffering, there are appropriate tools, but for some reason in the west, we often prefer to discuss complex subtle metaphysical statements we don't really understand¹, than to just go clean up the mess in the kitchen, which is a more pressing issue.
The only reason I'm even engaging in this kind of talk is to discourage others from approaching buddhism that way.
1: Because they are meant to be experienced, not thought about. Full disclosure, I only know what I don't know, and I don't fully understand them either.
Zen and Vajrayana practices can be an effective tool but I see more faulty thinking in its practitioners than people who stick to Sravakayana (Theravada + surviving canon of the other Early Buddhist schools).
Please don't promote sectarian strife here.
Perhaps more to the point, a quotation from Nanda-manava-puccha (as translated by Thanissaro Bhikku):
"Whatever brahmans & contemplatives describe purity in terms of views & learning, describe purity in terms of precepts & practices, describe purity in terms of manifold ways: none of them, living there in that way, I tell you, have crossed over birth & aging."
The Buddha is speaking very specifically in the quote you've mentioned of a class of religious priest, the brahman, and the contemplative engaging in jhanic meditations that do not lead to the ending of suffering.
You're right, the words of the Buddha weren't written down for hundreds of years after but across those earliest texts flung across space and time, we find an astonishing harmony.
Look, I'm seeing calls to end my supposed promotion of sectarian strife: I love Three Pillars of Zen, have obsessively studied the Mahayana epic the Surangama Sutra, and washed myself in the pure poetry of the Complete Reality school. But I cannot stress enough, and neither did the Buddha, in the importance of incisive, unequivocal language when it comes to identifying right view.
Vajrayana, the deeply mystical arm of Buddhism, stresses the importance of a guru relationship to the disciple, fraught with a history of sexual manipulation. Unquestioned power structures do this. We have thousands of years of history to support this.
Mahayana Buddhism gave birth to Zen, perhaps the cleanest strain to emerge but which sacrificed an essential tenet: that a monk should not grow their own food; should rely on the continuing generosity of the people to survive. It is further compromised by the trappings of rites and rituals, which the Buddha of the early texts rejected.
And what of Nichiren who famously declared that enlightenment was impossible in such a fallen world? The same enlightenment the pre-Mahayana Buddha stressed was for everyone?
Nothing, or better yet, no thing. They're just wrong.
Gautama was only one of the 33 buddhas, the last one so far. His entire life he was preparing to die and do so permanently in order to end the cycle of suffering.