Nonsense, the Romans loved Greek music. Moreover there would have been little to destroy--musical notation was still in its infancy in antiquity and most musical work would have been improvised or played from memory. We have only a very few fragments of notation, and the New Pauly sums it up well: "In Antiquity, music was passed on orally. Written music, nowhere mentioned explicitly in the literature of Antiquity, was the exception." Indeed, the reverse of your friend's statement is more true. Early Rome had a rich, developing musical tradition derived both from the Etruscans and more southerly Italian traditions, and Greek musical traditions largely replaced earlier Italian and Etruscan traditions, which survived mostly in comparatively minor theatrical and lyric performances deriving from native traditions. The great Greek poetic and musical traditions in tragedy and comedy, epic, elegy, and lyric by the late Republic had almost totally replaced native poetic and musical traditions among the highest class of artists and consumers, and little to nothing remains of what Italian traditions survived. Roman poets sometimes could prove quite adept at reshaping their Greek models--Catullus invented love elegy, and the neoterics wrote Greek-style verse in a way that neither Greeks nor Romans had really done before. But other times this was not so successful, and the situation could be quite complicated--the lyric traditions of Sappho and Alcaeus had more or less died out as a lyric form in Greek by the Hellenistic Period, and were revived (magnificentlt) by Horace (and not by any Greeks at all), only to never be picked up again by any other Roman poet

Yikes! I'm not a musicologist, but the broader claim, that Romans destroyed Greek culture.... whoah, man. Greek culture became the dominant elite culture of the Mediterranean. Rich Romans taught their kids Greek language, Greek philosophy, Greek rhetoric. Quintilian, one Roman rhetoric teacher, wanted his students to learn Greek before they learned Latin. When Christianity became a social force, its opponents didn't call themselves "Romans" but "Hellenes" - Greeks. The Easter Roman Empire, although calling themselves "Romans" (in Greek) spoke Greek and preserved Greek literature through the middle ages.

Greek poetic forms replaced traditional Roman forms. Saturnian meter is almost entirely lost. The Roman historical tragedy - praetexta - is almost entirely lost. If anything, Greek culture was knocking out the old Roman forms.

That makes no sense at all, as the Classicists already clarified.

The Romans took all the Greek music and theory they could, and some of that theory was kept alive in some way or another for several centuries after the fall of Rome.

We do not have a musical dark age because of the Romans. We don't know a lot about music in Antiquity because most musicians were not concerned with notation in the first place. In most cultures music is something you make now, not something you write down for the future. Most people have not been worried about writing this stuff down, it's been oral tradition all the way (it still is, even if we have a notation much more developed and widely taught than the Greeks').

We don't know much about the actual music in Antiquity. We know it was important in their lives, and we know philosophers dealt with it along cosmology, mathematics, ethics and what not (not to mention music and language were connected in a way we do not have now). The Romans preserved those texts, and studied them. The Muslims took some Greek texts with them when they conquered the south of Europe, and made all that theory available again (because they were able to translate from Greek to Arabic and then to Latin), but no music because there were no examples for them to keep.

In Western Music, we quickly get into prehistory. Modern notation was born inside a bureaucracy, it was created to fix and standardize music. And it took centuries for that technology to give us a clear picture of what was going on. Seriously, if we get back to say the 18th century, differences start to be noticeable enough for us to not be 100% sure of many details (but we still have a lot to work with). If you go back in time further than that, say the 15th century, it's an alien world with many unknowns even if we have a good bunch of examples. The 10th century? Oh, you are going to have a difficult time if you want to be sure about many things. And that's for a musical tradition that heavily depended on notation, there was also the music average people had in their lives (outside of big religious institutions or the houses of the super rich). It gets really tricky to know what that music was like because most people were not writing it down. No Romans or anybody else there to destroy it intentionally.

This weird thing we do now, preserving and reviving music from the past, it's rather new. It was normal for music to get lost into darkness, it was normal for it to stop existing after it was played.