Now correct me if I am wrong. The comparative method suggests that theos and dyeus are not the same because "strict application" would suggest that instead of theos we would have deos or something to that effect.
Only if one is applying the "comparative method" to these two lexemes (I would say methods but then Baldi is the expert here, not me). That is, granted only the application of the "comparative method" of Greek and Latin and the two relevant lexemes we would have only what Baldi describes. However, if applied merely to the two languages in their entirety, let alone IE language in general, we can determine far more. Greek has a word that, like the Latin
deus, can be traced back to PIE. However, that lexeme isn't
theos but Zeus. In other words, we know the Greek equivalent of
deus and we also know that the reconstruction methods we have successfully used since the late 1700s show that the Greek
theos isn't related to any PIE root for "god" or anything else.
But with this said, Greek writing began around 800b.c. and there is no written account of how the Greek said God prior.
Actually one of the great breakthroughs in classical philology, IE linguistics, historical linguistics, etc., was the realization that the previously undecipherable Linear B texts were Greek but in a different alphabet. So not only do we have a record of Greek going back even farther, the earliest extant representations of the language use completely different alphabet, allowing us to examine phonological, lexical, and other aspects of ancient Greek that are impossible for most ancient languages.
But, the mouth movement is close, and the sound is close, and it could be from the same roots, but we don't know for certain, because it doesn't fit the mold so it could also be chance.
The sound is less close than one might think. Like Chinese, Greek was a tonal language. So while neither I nor anybody I know pronounces any ancient Greek dialect the way we think it is pronounced (and in fact my first professor of ancient Greek was Greek and used modern Greek pronunciation which made life difficult for me), we still know that e.g., the theta which begins the word
theos was aspirated and the zeta that begins zeus was phonologically distinct from this but related to the dental initial pronunciation of
deus and the PIE root.
But is it erroneous to say they are not from the same roots, since they could be?
It would be erroneous to say it is impossible for them to have the same root. But the sciences are about the likely and in particular the likely vs. the extremely unlikely, and here we have a situation that is extremely unlikely (that
theos and
deus share the same root) and one that is likely (they don't).