Rogers was unfazed precisely because he possessed two precious, rare cards.
One was a Team Dismissal Card, SS-level, which allowed him to attack allies without penalty. Being a Fourth-order Hero himself, if used well, he could completely launch a surprise attack and kill another Fourth-order Hero. The Individual Exemption Card he obtained after killing a Russian team leader was the most valuable of his spoils of war.
The Individual Exemption Card, an SS-level rare equipment, permitted the user to leave the game and return to the Trojan Room even if the mission failed, but it required him to accept severe penalties; his physical abilities would be reduced by two-thirds, and he would be restricted from using his highest-level props in the next round.
Even if used before mission failure, he still had to accept a penalty, though it was half as severe as if it were used after failing.