John,
I have been thinking much about your post since I first read it. Your question: "It makes me wonder, what do well intended christians think that they have to inject the 'God equation' into situations like this" haunts me, still. I answered it based on my experience. Now I would like to share another scripture.
2Corinthians 1:3-7 NASB:
3Blessed be the God and Father of our Lord Jesus Christ, the Father of mercies and God of all comfort,
4who comforts us in all our affliction so that we will be able to comfort those who are in any affliction with the comfort with which we ourselves are comforted by God.
5For just as the sufferings of Christ are ours in abundance, so also our comfort is abundant through Christ.
6But if we are afflicted, it is for your comfort and salvation; or if we are comforted, it is for your comfort, which is effective in the patient enduring of the same sufferings which we also suffer;
7and our hope for you is firmly grounded, knowing that as you are sharers of our sufferings, so also you are sharers of our comfort
It continues with a testimony:
8For we do not want you to be unaware, brethren, of our affliction which came to us in Asia, that we were burdened excessively, beyond our strength, so that we despaired even of life;
9indeed, we had the sentence of death within ourselves so that we would not trust in ourselves, but in God who raises the dead;
10who delivered us from so great a peril of death, and will deliver us, He on whom we have set our hope. And He will yet deliver us,
11you also joining in helping us through your prayers, so that thanks may be given by many persons on our behalf for the favor bestowed on us through the prayers of many.
I suggest you allow this scripture minister to you.
Now for an observation: people who do not accept the divine component in affliction will find themselves embroiled in bitterness against God for allowing it. When Christians inject the God factor in their conversations with the afflicted, rarely will this idea be a new one - it will be one they already are wondering about, struggling with. It is true some Christians are too flippant about it and that is tragic. But even so, one can learn from it even if it was not well spoken.
If one is concerned about the spiritual outlook of the victim, you could always ask him/her how they feel about this calamity and go from there - allowing the victim to express his feelings on the matter. If you have gained the trust of he victim you can minister to this heart's need.
If you study Isaiah and Revelation one will soon begin to understand that God sends afflictions to destroy people's security in things around them; that life is fragile and can easily be snuffed out. Until this becomes a reality understood, one is not ready to live - as in really LIVE!
Blessings..