That is Woodfill's word, not Armstrong's or Aldrin's. Faith in God may have been a part of Armstrong's and Aldrin's lives but they didn't rely on it to get to the moon. And yes, only an idiot would have climbed into that rocket with nothing but faith.
God gave them the intelligence and ability to ask and learn what they needed to know to lower the risks they faced. They asked the questions and learned as much as they could before starting out on their journey. Only an idiot would do otherwise.
The principle is summed up in the old adage - "God helps those who help themselves."