Curiously, you don't hear the legions of rescuers complaining that giving thanks to God takes away from their contribution; rather, most of them seem to be glad to have been involved in something that that drew its inspiration from faith and trust in God as well as their own skills and commitment.
I think the bit about God getting credit for good things and dodging the blame for bad things rather works the other way round. We see things like this, where courage, commitment, working together, hoping and believing even against the odds, shared patience in suffering, mutual support in community, the joy of reunion, a sense of life out of death are values which we accept as good and positive. In a universe which seems indifferent to such things, and treats us so often to disasters and catastrophes (to which humans add with great enthusiasm in the name of tribe, religion, politics or just for the hell of it), we dare to make this distinction that says these things are good, they have real value. And yes, for some of us at least, those are the values we see in God.
Of course, it might just be that we project these things onto the blank screen of the idea of God. Or (in a determined way) don't bother even with the idea of God except to ridicule it. But it may also be that our understanding of these values is derived from, or is a reflection of, the reality of God.
I'm with those who are quite happy to give thanks to God for the safe rescue of a few trapped miners, the efforts, determination, skills and commitment of their rescuers, and a few moments of joy and exuberance in an often much darker world.