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, a classical 以 + 为 frame meaning 'take as/consider to be'.
