The Devil

No, we are not. We are shown flashes of their evil deeds. What would be the point of that if it turned out those flashes were fake? Your theory assumes the writer didn't have a clue about storytelling.

Do you think Agent Doyle wouldn't have said anything to defend himself if he hadn't actually killed his mother?

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We do know the people did bad things. The scene at the end shows Agent Doyle asking Adam how Adam knew when he gets the flashback of Agent Doyle killing his mother. Making the excuse that it was a coincidence would make no sense. The story is written purposefully to demonstrate Adam and his father were right the entire time. That is what makes the story so interesting and unique, as well as a great horror mystery thriller.

Even the scenes showing how Adam couldn't be recognized by the security cameras and the other agent act as proof that Adam and his father did indeed have a mission from God.

I think you might be right. We only hear the story from one point of view, perhaps the father and Adam were the real "demons" because they murdered people. Maybe the lesson was that taking a life is wrong regardless of the crimes someone committed. In the end, maybe only God has the right to make that call.

There was another post I read in the message boards where someone said that the film showed evidence that Adam and the father were acting out God's will (for example, the scrambled video footage at the police station.) Technically, the "devil" could accomplish the same thing so, there is a possibility that "God" was not the one asking for these murders to be carried out.