My take on it is in life there are realities (such as earth, wind, body, mind, sky, etc) & these realities will play a part in most attempts to describe the world & life. Therefore, most philosophies will share certain phenomena in common.
For example, reading The Brihadaranyaka Upanishad, Section II - The Process of Creation, there are verse which sound very much like the Old Testament creation story in Genesis, particularly the use of the phrases: “In the beginning” & “Let there be” and the overall differentiating of the undifferentiated via “naming” or “calling”:
There was nothing whatsoever here in the beginning. It was covered only by Death (Hiraṇyagarbha), or Hunger, for hunger is death. He created the mind, thinking, ‘Let me have a mind.’ He moved about worshipping (himself). As he was worshipping, water was produced. (Since he thought), ‘As I was worshipping, water sprang up,’ therefore Arka (fire) is so called. Water (or happiness) surely comes to one who knows how Arka (fire) came to have this name of Arka.
Water is Arka. What was there (like) froth on the water was solidified and became this earth. When that was produced, he was tired. [Page 27] While he was (thus) tired and distressed, his essence, or lustre, came forth. This was Fire.
He (Virāj) differentiated himself in three ways, making the sun the third form, and air the third form. So this Prāṇa (Virāj) is divided in three ways. His head is the east, and his arms that (north-east) and that (south-east). And his hind part is the west, his hip-bones that (north-west) and that (south-west), his sides the south and north, his back heaven, his belly the sky, and his breast, this earth. He rests on water. He who knows (it) thus gets a resting place wherever he goes.
In Section VI - The Three Aspects of the Universe, there is a discussion about ‘nama-rupa’, which while being a valid descriptor of how the human mind constructs its world, does not necessarily mean the Buddha’s use of ‘nama-rupa’ was always & predominantly the same:
This (universe) indeed consists of three things: name, form and action (trayaṃ vā idam—nāma rūpaṃ karma).
Of those names, speech (sound in general) is the Uktha (source), for all names spring from it. It is their Sāman (common feature), for it is common to all names. It is their Brahman (self), for it sustains all names.
Now of forms the eye (anything visible) is the Uktha (source), for all forms spring from it. It is their Sāman (common feature), for it is common to all forms. It is their Brahman (self), for it sustains all forms.
And of actions the body (activity) is the Uktha (source), for all actions spring from it. It is their Sāman (common feature), for it is common to all actions. It is their Brahman (self), for it sustains all actions.
These three together are one—this body, and the body, although one, is these three. This immortal entity is covered by truth (the five elements): The vital force is the immortal entity, and name and form are truth (nāmarūpe satyam); (so) this vital force is covered by them.
Then Section IV - The Creation and Its Cause it introduces the ideas of: (i) the organ of speech; (ii) the mind; and (iii) the vital force, which are very similar to the kaya, vaci & citta sankhara, defined in MN 44 as breathing, applied thought & perception/feeling, and also found as terms in dependent origination:
This (universe) was then undifferentiated. It differentiated only into name and form—it was called such and such, and was of such and such form. So to this day it is differentiated only into name and form—it is called such and such, and is of such and such form. This Self has entered into these bodies up to the tip of the nails—as a razor may be put in its case, or as fire, which sustains the world, may be in its source. People do not see It, for (viewed in Its aspects) It is incomplete. When It does the function of living, It is called the vital force; when It speaks, the organ of speech; when It sees, the eye; when It hears, the ear; and when It thinks, the mind.
Then Section V - Manifestations of Prajapati continues:
‘Three he designed for himself’ means: The mind, the organ of speech and the vital force; these he designed for himself… Prāṇa, Apāna, Vyāna, Udāna, Samāna and Ana—all these are but the vital force. This body is identified with these—with the organ of speech, the mind and the vital force.
These are the three worlds. The organ of speech is this world (the earth), the mind is the sky, and the vital force is that world (heaven).
These are the three Vedas. The organ of speech is the Ṛg-Veda, the mind is the Yajur-Veda and the vital force the Sāma-Veda.
These are the gods, the Manes and men. The organ of speech is the gods, the mind the Manes, and the vital force men.
These are the father, mother and child. The mind is the father, the organ of speech the mother, and the vital force the child.
In conclusion, my point is just because this Upanishad identifies the phenomena of vital force (kaya sankhara), speech (vaci) and mind (citta) and groups them together as constituents of creation, does not mean the Buddha used these as a blue print for any of his teachings, including dependent origination.
The body as a reality contains breathing, the mind contains thought function, perception & feeling. When these basic phenomena are affected by ignorance & defiled asava (outflows), these phenomena then lead to conditioning the body & mind to generate stress & suffering.
For example, the science of Traditional Chinese Medicine (TCM) understands an impure, polluted or blocked vital force (chi; prana) can cause physical & mental disease. Just because the vital force is mentioned in the Upanishad does not mean theories of TCM were based on the Upanishad.