O'Brien is successful in this piece and in much else that he writes because he knows how to use words very effectively. The phrasing here is direct, colloquial, intimate, familiar, and for all these reasons credible. The work conveys the complexities of war in a way that a much more elaborate style would fail to do. (It is hard to imagine Henry James writing an effective war story.) Simply as a stylistic tour de force, this is an effective story.
O'Brien certainly captures the horrors of war and makes his readers get at least a glimpse of what these soldiers had to endure during the Vietnam war. The length of the first chapter and the tedium of the lists of the "things they carried" mimics the weight and tedium of their daily existence. Was he 100% telling the truth? Maybe, maybe not, but it doesn't matter because he succeeds in making his audience feel it. Whether the group actually killed the baby water buffalo or not doesn't matter -- that story captures the frustration and pent-up anger of the men better than any direct telling of those feelings ever would. That is O'Brien's point: sometimes the truth is not as "true" as a story in capturing the essence of a situation.
When I read this story, I can't help but imagine the movie Saving Private Ryan where the confusion of the day--location of men, flying of bullets, people drowning from the weight of their own equipment--is present in O'Brien's imagery-packed story. As the posts above mention, it's so confused and horrible, it has to have truth behind it.
I think this story succeeds in presenting readers, the majority of whom have never experienced a war-type scenario as O'Brien has, with the confusing, contradictory and overwhelming presentation of war that O'Brien tries to stress. In a sense, as one of the above posts makes clear, O'Brien is writing this story not to be read by us, but to try and help him make sense and somehow order the chaotic conglomeration of thoughts and ideas that make up war fiction. He succeeds very well in presenting this image to us.
There also comes a place in stories like these, particularly those about war and combat, where the reader thinking to themselves, "there's no way I could survive or understand something like this". For the average person, such experiences go far beyond even the most traumatic events we have ever endured. In part, this is why America is such a warrior society, because the people who do the fighting and dying do things we could never imagine ourselves doing. Thus, we idolize them in both tangible and intangible ways. O'Brien is a master storyteller, but he couldn't do it without the truth behind him.
O'Brien also states that a true war story is recognizable in its use of details as well as its level of "unbelievability"; the more unbelievable it is, the more likely it is to be real. His story "Sweetheart of the Song Tra Bong" is probably the best example in the text of a "true" war story in that it is riddled with specific details and the sheer unbelievability of it is what makes it believable. Furthermore, he states that a true war story does not need true facts but instead finds its truth in the emotion it provokes in the listener/reader. A true war story is felt in the gut. According to this, his stories in The THings They Carried could not ring truer because of the emotion they express. All of the stories raise the question of how war dehumanizes its participants in different ways and hone in on the emotion of the soldiers. Finally, a true war story isn't about the war according to O'Brien; most of his stories in the book are nto about the fighting nor the war, but moreso the experiences of the troops before, during, and after the war and how it is that the war infiltrates all of these experiences.