He listened to the rumor and took it as the truth.
Tips
usage
Typically suggests being fooled — the speaker takes something false for true. Often paired with 玩笑, 谎言, 谣言. Context usually makes the gullibility explicit.
grammar
信以为 X = 'believe it to be X'. Parallel with 引以为戒 and 自以为是 — classical 以 + 为 frame meaning 'take as/consider to be'.
