That's something of an exaggeration, I recently wrote a comment here relating to it. Both war cries and the beating of weapons against armor are well-attested--Polybius even goes so far as to say that it's a custom of the Roman people to hit their shields with their swords, something that Greeks of his time no longer did.

More unsettling than a totally silent formation appears to have been a formation that raised a single great war cry--this is something that the Romans did well into the Principate, and Caesar thinks that allowing your troops to raise a big old war cry all at once is one of the great advantages of an attack, throwing your enemies off balance and inciting your troops to attack with more force. Xenophon relates that the Ten Thousand deployed in silence at Cunaxa while the Persian infantry shouted and clashed their weapons as they deployed, before letting out a single great shout that put the Persians to flight.

But not only is it well-attested that the Romans would customarily let out, at the very least, a single shout in unison at the beginning of an advance or before throwing their javelins (Caesar frequently mentions war cries being raised at this latter point), but this tactic is well-attested long before the Romans. The Greeks were doing this since the Persian Wars at least, and Greek armies appear to have deployed silently throughout most of the historical period, although they often marched forward to rhythmic war cries (the Athenian "eleleu eleleu" and Spartan "a la la la" being the two most famous).