You have to understand the chronology of sound shifts. In Proto-Balto-Slavic PIE *o merged to *a. Later on, Proto-Slavic did the reverse by shifting Proto-Balto-Slavic *a to *o. In contrast, the *a in modern Slavic derives from earlier Balto-Slavic long *ā. And as I said, the *a > *o sound shift in Balto-Slavic happened during the Migration Period. Latin loanwords, as I mentioned, are subject to the latter sound change. "asellus" (donkey) > "osel", "acetum" (vinegar) > "otset". The same applies to /a/ found in Germanic loanwords (in contrast, the Germanic *ō was generally rendered as *ū into Proto-Slavic ("u" in modern Slavic), whence *bōk- 'beech' yielded Slavic *buk). I might add that, to my knowledge, there's no evidence really old language contact between speakers of Proto-Slavic and Greek, which - for example - very much exists for Albanian with Greek (e.g. "mēlo" or "μηλο" > "mollë"). Now Thrace was a region that was thoroughly hellenized already from fairly early, if Proto-Slavic speakers were really present there, we should see an ancient stratum of Greek loanwords.
The same definitely did not happen in Phrygian or Thracian, as these languages preserved Proto-Indo-European /a/ and /o/ as distinct vowels. This is why neither Phrygian nor Thracian, despite being Satem languages, were supposedly close related with Balto-Slavic.
What I would like to add is that there can be no doubt is that during the classical Antiquity, the speakers of Proto-Slavic would have to be located outside of the Roman Empire. If there was, we should see place names, personal names, etc. from the Roman period in Roman sources. We don't, and Curta for one should have been aware of this, which is why his proposal is so absurd, and why its more sensible to place the Proto-Slavic homeland outside of the Roman Empire (which takes us back to Chernoles or Milograd as the most likely choices).
