Vism. 16APS breath meditation step 3 crime

The translation of the sutta passage for 16 APS breath meditation instruction is correct, in that they translate kāya as 'body'.
He trains thus: “I shall breathe in … I shall breathe out experiencing the whole body”: 

The crime is in redefining the meaning of 'body' to mean something completely different than what it means in all the other kaya anupassana exercises (see MN 10 and MN 119), where kaya is always the anatomical body.

Vism. 16APS breath meditation step 3 

171.(iii)  He trains thus: “I shall breathe in … I shall breathe out experiencing the whole body”: he trains thus: “I shall breathe in making known, making plain, the beginning, middle and end (footnote 48) of the entire in-breath body. I shall breathe out making known, making plain, the beginning, middle and end of the entire out- breath body,” thus he trains. Making them known, making them plain, in this way he both breathes in and breathes out with consciousness associated with knowledge. That is why it is said, “He trains thus: ‘I shall breathe in … shall breathe out …’”

172. To one bhikkhu the beginning of the in-breath body or the out-breath body, distributed in particles, [that is to say, regarded as successive arisings (see note 45)] is plain, but not the middle or the end; he is only able to discern the beginning and has difficulty with the middle and the end. To another the middle is plain, not the beginning or the end; he is only able to discern the middle and has difficulty with the beginning and the end. To another the end is plain, not the beginning or the middle; he is only able to discern the end [274] and has difficulty with the beginning and the middle. To yet another all stages are plain; he is able to discern them all and has no difficulty with any of them. Pointing out that one should be like the last-mentioned bhikkhu, he said: “He trains thus: ‘I shall breathe in … shall breathe out experiencing the whole body.’”
173. Herein, he trains: he strives, he endeavours in this way. Or else the restraint here in one such as this is training in the higher virtue, his consciousness is training in the higher consciousness, and his understanding is training in the higher understanding (see Paṭis I 184). So he trains in, repeats, develops, repeatedly practices, these three kinds of training, on that object, by means of that mindfulness, by means of that attention. This is how the meaning should be regarded here.

footnote 48. 

The beginning, middle and end are described in §197, and the way they should be treated is given in §199–201. What is meant is that the meditator should know what they are and be aware of them without his mindfulness leaving the tip of the nose to follow after the breaths inside the body or outside it, speculating on what becomes of them.