EDIT, TL;DR: if the only contrast between 2+ stop series is VOT, they won’t switch places. Either Greek or Armenian did so, so at least one PIE stop series has a secondary articulation for sure.

However the traditional reconstruction assigns breathy voice to this secondary articulation, creating a highly unstable system for PIE that would almost certainly not survive as late as Proto-Graeco-Armenian.

Sorry beforehand for the wall of text.

The currently proposed phonological system for Proto-Indo-European has three series of stop consonants:

• unaspirated - *p t k ḱ kʷ
• voiced - *b d g ǵ gʷ
• breathy voiced - *bʰ dʰ gʰ ǵʰ gʷʰ

This system is not directly attested in any of the children languages. In fact, it is not attested at all; there’s a language from Borneo called Kelabit that uses something similar-ish, but that’s it. This lack of attestation happens because because breathy voiced consonants are complex to articulate, and… well, humans are lazy, if we can convey a contrast without a complex articulation, we do.

And different child languages would have handled the situation in different ways:

• Celtic - merging breathy voiced stops into the plain voiced ones: t d dʰ → t d d
• Italic - transforming the breathy voiced stops into fricatives: t d dʰ → t d ð; eventually Latin would transform that *ð into *θ and then *f, Cockney style
• Greek - transforming the breathy voiced stops into more common aspirated stops: t d dʰ → t d tʰ
• Germanic and Armenian - unaspirated becomes aspirated, plain voiced becomes unaspirated, breathy voiced becomes plain voiced; t d dʰ → tʰ t d. Then Germanic fricativises the aspirated series, tʰ→θ.
• Sanskrit - introduce a fourth series of stops (aspirated), so the breathy voiced series get a symmetrical voiceless series, reinforcing its presence in the phonological system. The complexity is still there but it’s “justified” by the presence of a similar articulation, for more contrasts.

So far, so good, right?

Well. If Greek and Armenian are closer to each other than they are to other IE branches, this means that Proto-Graeco-Armenian existed. And that it inherited that *t d dʰ system. That, as I said, is highly unstable and unattested… like, we can give a pass to a weird system surviving just enough so its descendants get rid of it, but having that weird system survive for likely centuries, perhaps millennia? It’s likely bullshit.

Now let’s talk about voice onset time, or VOT. VOT can change over time; however, consonant series distinguished only by VOT will never “switch places” - because once the VOT of both series gets similar enough, they’ll simply merge. So for example:

• [t d] → [t t] // OK, both series merged
• [t d] → [tʰ t] // OK, series are still distinct but both raised VOT
• [t d] → [d t] // nope, that won’t happen

(Note: I’m using only [tʰ t d] for the examples, but the reasoning is the same for [pʰ p b] or [kʰ k g] etc.)

The same applies if you have three series of consonants, instead of two; you typically don’t see a “merry-go-round” like [tʰ t d]→[t d tʰ], because once that last series increases its VOT, it’s bound to merge with the second series.

…and yet if you look only at Ancient Greek and Armenian, it’s like one of them did the above - because Greek /tʰ/ (highest VOT) corresponds to Armenian /d/ (lowest VOT).

The only way to switch the places of the series is if their distinction is not just based on VOT, but also something else, at least temporarily. Like… breathy voice.

Are you noticing the contradiction? It’s like we need a bullshit system to survive for a huge period of time, enough for Proto-Graeco-Armenian to be able to inherit it.