Why the meditation on in breathing and out-breathing shouldn’t be complicated by where one places one’s focus.
In the initial stages of one’s contemplation of breath, the following becomes obvious: the body relaxes with conscious awareness of in and out breathing.
I think that as long as one consciously observes one’s breath, one is practicing the contemplation. I think there’s a good reason why we should hesitate to indoctrinate the contemplation of breath with a focus on one’s nose-tip. I think that as long as the contemplative is focusing on his or her breath, he or she is benefiting from the practice.
The practice essentially trains one to focus only on one’s breath; apart from all other distractions. As breathing is primarily the most essential thing, in an outwardly sense, that a person does in order to survive, meditation on breath directs just such a person towards their most elemental “mode” of being, and removes them from the distractions of an ad hoc existence, where things which should not matter actually do (in the confused mind of us people in our "worlds").
It’s an overstatement to assume that people will be taught to focus on one’s nose in this practice simply because in Buddhaghosa’s commentary and exposition: Path of Purification, he made it a point to say just this. There are likely many people who have attempted mindfulness of breath in a variety of ways only to conclude that the nose-tip is the quintessential focus for the contemplation, having reached a certain level of accomplishment with this certain kind of focus (and not some other kind of focus).
My gratitude towards Bhikkhu Pesala, for the link to the late Venerable Mahāsi Sayādaw of Burma's exposition describing a practice which emphasizes focus on the diaphragm, in the thread "So I've Got a Foul Set of Legs".
Reading through the late Venerable Mahāsi Sayādaw's short exposition, it appeared to me that many, but not all, of the applications of mindful breathing which are encouraged in the traditional description of the practice (as it is perhaps understood by the majority out there to center on the tip of the nose), with such modes as: eating, walking, bending one’s limbs, urinating, excreting, etc. overlap with a focus on the diaphragm.
Because it is simply the case that when breathing, awareness leads to relaxation - I think it’s fair to suggest that the original sutta on the contemplation can be interpreted with a focus on either the tip of the nose or the centre of the lungs, or the diaphragm itself. In other words, as appicchato mentioned, as long as one "knows" that he is breathing in or he is breathing out, he is practicing the contemplation. It does not matter where one "knows" he is breathing at:
But only if the method allows for the prescribed outcomes. I cannot attest to anything beyond a manifestly impermanent, decaying sense of my body in my attention to breath, so I have no way of knowing if the method leads to all outcomes. I can make a certain kind of statement however.
Attention to the diaphragm ties one to the process of breathing where it manifests physically. Attention to the nostrils ties one to the process of breathing where it manifests in the senses. So there is a pretty big difference in the nature of one’s attention in each of these cases.
With attention to the diaphragm one may experience a relaxing of one’s body in a very physical way; owing to the attention paid to the breathing process. But attention to the air as it comes in and out of the nostrils puts emphasis on the sensation of breathing (not the physical determinant). So, the progress towards a state of understanding that emphasizes a fabricated reality (based on the senses) might only be possible with the awareness of breathing as it relates to sensation and not kinematics.