The Truth referred to above is the Truth of God, this Truth is not of this world and therefore forever true. The Truth of God when properly accepted answers all questions. It will never raise any further questions. If it raises any questions at all it is either not the Truth of God or you're just unable to accept it at that point in time.
The truth that you're referring to is the truths of the world. These can never bring peace because they're not forever true. They are only true for a time being before being invalidated. In your example, being diagnosed with cancer is certainly frightful because that is a truth of the world and not the Truth of God.
Distinguishing between the so called truths of the world and the Truth of God is fundamental in any spiritual pursuits. The truths of the world are concerned with worldly and bodily matters. The Truth of God is that there is no world, no body, and that you're pure spirit.