[svat]

This argument is circular: it is only Western indology that defines “Vedic” as referring to “the actual Vedas” by which it means only the saṃhitā portion of the texts. The traditional Indian understanding of “Veda” is indeed that it includes both mantra (saṃhitā) and brāhṃaṇa — the latter including āraṇyaka and upaniṣad. Yes it's true that sometimes when (say) “Ṛgveda” is mentioned, in that context it may refer only to the ṛk saṃhitā, etc — but the narrow meaning is only contextual; in general one talks of which brāhmaṇa-s / āraṇyaka-s / upaniṣad-s belong to which Veda, etc.

More generally the Vedāṅgas are also considered part of the Veda, etc. When Pāṇini (whom you allude to in one of the replies here) distinguishes the older language, he uses terms like “chandasi” not "in the Vedas”. Even today when a certain practice or person is called “Vaidika” obviously it doesn't mean a certain time period, belonging to several centuries BCE.

Ultimately, to consider linguistic analysis relevant to the definition of “Vedic” and to say “to lump them into one is incorrect, even if that is the tradition” is simply saying “let's make up a definition of ‘Vedic’ different from the traditional definition, under which the traditional definition can be termed incorrect” — no traditional scholar thinks of “Vedic” as referring to “the Vedic language” as referring to the language of the saṃhitās.

Edit: I have a theory for how this state of affairs came about: Western interest in Sanskrit texts took off in a big way after William Jones's (much-quoted) pronouncement of the relation between Sanskrit and Persian and Greek and Latin. So the interest started with linguists and philologists, who were naturally more interested in the oldest texts / the texts whose language was closest to the rest of the Indo-European family, and that has become the frame by which these texts are still talked about (rather than say the framing used by traditional Vaidika paṇḍita-s). This is why we see someone confidently deciding that linguistic analysis can tell us something about what “Veda” means or should mean, rather than only telling us about the language of a certain subset of texts.