In Plutarch, Marcellus, XXVI, 1 it seems that one single scarlet tunic is displayed announcing the incoming battle, not that every legionary wear a scarlet tunic. We can say that nobody wear one, if it was so evident when one single scarlet tunic was desplayed.

The meaning of red: consul Decio Mure wore a red band when he trew himself into the enemy line in sacrifice to win the difficult battle of Sentino (295 BC): if so is written, it means that it was important.

The color of tunicae: yes, they had red bands, but i think that you should not see them as a normal cloth. They where sacred clothes to be used in Senato, wich was a sacred place for the Romans. So i think it's possibly for that reason that they had a red band.