Question: Why was Oliver so quick to believe Annie's friends when he was told she was in danger?
Answer: Think of the circumstances. A group of obvious orphans shows up at your house at night, saying they are friends of Annie. Warbucks knows how far the orphanage is from his home since he went there earlier. Annie believed her parents were already dead, as so many people showed up claiming to be them but didn't have the locket. Annie was very hesitant and unreceptive toward the ones who showed up to bring her home. Warbucks also caught a bad vibe from the fake parents when it came to giving them the reward check. It's not hard to believe that he would instantly realise that he was scammed and Annie is in trouble.
Answer: They're disguised because they are committing a crime by falsely claiming the reward.
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