Mindfulness directed to the body: the 6 doors

Sometimes I read comments or books that suggest mindfulness of the body is only related to the body door.
This sutta explains it in relation to the 6 doors, the salayatana.

Samyutta Nikaya ( Bodhi translation)
247 (10) The Simile of the Six Animals

Bhikkhus, suppose a man with limbs wounded and festering would enter a wood of thorny reeds,218 and the Kusa thorns would prick his feet and the reed blades would slash his limbs. Thus that man would thereby experience even more pain and displeasure. So too, bhikkhus, some bhikkhu here, gone to the village or the forest, meets someone who reproaches him thus: ‘This venerable one, acting in such a way, behaving in such a way, is a foul village thorn.’ Having understood him thus as a ‘thorn,’ one should understand restraint and nonrestraint.219 “And how, bhikkhus is there nonrestraint? Here, having seen a form with the eye, a bhikkhu is intent upon a pleasing form and repelled by a displeasing form. He dwells without having set up mindfulness of the body, with a limited mind, and he does not understand as it really is that liberation of mind, liberation by wisdom, wherein those evil unwholesome states cease without remainder. Having heard a sound with the ear … Having cognized a mental phenomenon with the mind, he is not intent upon a pleasing mental phenomenon and not repelled by a displeasing mental phenomenon. [200] He dwells having set up mindfulness of the body, with a measureless mind, and he understands as it really is that liberation of mind, liberation by wisdom, wherein those evil unwholesome states cease without remainder. It is in such a way that there is restraint. “Suppose, bhikkhus, a man would catch six animals—with different domains and different feeding grounds—and tie them by a strong rope. He would catch a snake, a crocodile, a bird, a dog, a jackal, and a monkey, and tie each by a strong rope. Having done so, he would bind them to a strong post or pillar. Then those six animals with different domains and different feeding grounds would each pull in the direction of its own feeding ground and domain. The snake would pull one way, thinking, ‘Let me enter an anthill’ … (as above) … The monkey would pull another way, thinking, ‘Let me enter a forest.’ “Now when these six animals become worn out and fatigued, they would stand close to that post or pillar, they would sit down there, they would lie down there. So too, bhikkhus, when a bhikkhu has developed and cultivated mindfulness directed to the body, the eye does not pull in the direction of agreeable forms nor are disagreeable forms repulsive; the ear does not pull in the direction of agreeable sounds nor are disagreeable sounds repulsive; the nose does not pull in the direction of agreeable odours nor are disagreeable odours repulsive; the tongue does not pull in the direction of agreeable tastes nor are disagreeable tastes repulsive; the body does not pull in the direction of agreeable tactile objects nor are disagreeable tactile objects repulsive; the mind does not pull in the direction of agreeable mental phenomena nor are disagreeable mental phenomena repulsive. “It is in such a way that there is restraint. “‘A strong post or pillar’: this, bhikkhus, is a designation for mindfulness directed to the body. Therefore, bhikkhus, you should train yourselves thus: ‘We will develop and cultivate mindfulness directed to the body, make it our vehicle, make it our basis, stabilize it, exercise ourselves in it, and fully perfect it.’ Thus should you train yourselves.”