I have one piece of supporting evidence from within the sutta itself, which is that at the very end, the three doctrines that the Buddha says he refutes with this talk are:
(C ) nihilism
which match up to the views in (1), (2), and (3) above as follows:
(A) causality is the Brahmin's view of the cosmos, based on correspondence (“As above, so below; as below, so above”) the causality being that what's done in ritual has an effect on the world above and so below. (See references at the end of this post.) So “non-causality” is a denial of the Brahmin's view, and this matches perfectly with “Nothing given, nothing offered, nothing sacrificed” as a catch-phrase.
(B) non-doing: I expect you're aware that the Buddha took the world “kamma” which meant “action” and shifted it over to mean “intention”. The doctrine being denied here is “kamma as action” (not the Buddha's kamma) – the doctrine of non-doing, then, is a denial that action had any effect on life after death. The Vedic philosopher Yajnavalkya, whose parts in the Upanisads the Buddha references, was quite famous for stating that the atman was not touched by the actions of the body-mind complex, so that is one well-cited example of a doctrine of non-doing that the Buddha was familiar with because it was being discussed in his day.
(C ) nihilism: what is that long list of “no this, no that” but an excellent example of the nihilist's view of things, denying that everyone else's worldview is correct because none of that stuff is true at all.
'Dimensions of the Sacred: An Anatomy of the World's Beliefs' by Ninian Smart (1999) wrote: It may be noted that sacrifice typically involves the notion of transformation, for instance the change of status of the animal or other offering to become something sacred, with the domain of the god, and its transfer to another sphere, for instance through the agency of Fire or Agni.
The notion of transformation serves as the basis of one of the two major theories of causation in Indian philosophy.
'Reflections on Resemblance, Ritual, and Religion' by Brian K Smith (1998) wrote: The doctrine of counterparts makes possible not only ritual efficacy – the manipulation of ritual counterparts in order to influence cosmic prototypes – but also ritual efficiency.