Are you asking about marines or rowers? The vast majority of the people on any warship would be unarmed and unarmored rowers huddled below decks on their benches. Marines, however, were most certainly heavily armored and armed, that is well accepted. Both the Greeks and the Romans essentially employed exactly the same troops as would operate on land on board their ships--among the Romans even the organization of marine units mirrored legionary organization. We have multiple visual representations of marines, which are nearly indistinguishable from regular legionaries, and we have many literary references--Livy, for example, mentions Scipio using his marines alongside his infantry, without rearming them or anything. In ancient naval warfare purely ramming was rarely sufficient to sink a ship outright, and even so a ramming action would result in a tangle. Boarding actions are the norm, and both the Greeks and Romans employed heavy infantry as their marines--Thucydides, for example, rarely uses the word for marines (ἐπιβάτης) even when it's abundantly obvious that he must be referring to marines, but instead simply says hoplites. There's not really any debate on this--Thucydides, for example, gives us the compliments of rowers, crew, archers, and hoplites on board each trireme in the Athenian fleet, and we know that during the Principate marines were frequently used as regular infantry forces, as fleets were frequently posted away from legionary camps

You would be surprised how many men out to sea right now who cannot swim. It is considered that if you went overboard, you were doomed and had little chance of survival.