It's fine to be wary. It's dumb, naive, or reckless not to do the work and analyze whether or not the fear is warranted in a specific case. Adam Curtis did the work in a specific case and found the fear unwarranted for that specific case. Parading that example has no fucking relevance for this specific case except to say that someone always has an incentive to lie about something.

The people abiding by the principle "strive for peace, prepare for war" are not "scary scared people" despite being very afraid of war on some level.