I think the quick answer is probably be going to come for a theist that 'one shall not put the Lord your God to the test'. If that were the case, then of course god would ignore the test and nothing would be proved.
In the case of Jeanna Giese there is a more mundane explanation for here cure and it has nothing to do with god. The doctor treating here put her into a coma on the basis that the comatose brain would not be affected, as normal one, with the rabies bug. Good scientific reasons and it worked. The prayer circle was something for the people to do whilst medicine cure here.
I find it quite interesting that Jeanna Giese, was cured after all that prayer. Apparently all the prayers before did not work for those afflicted with Rabies, but this set of prayers was so compelling that god decided he would let people occasionally live as long as they used the Milwakee Protocol.
Thank you Jeanna Giese for your finally catching gods ear he was even so benevolent as to only give her minor brain damage. Perhaps we can pray just a little more and have the milwakee protocol work 80 or 90% of the time with even less brain damage.
directly commenting on the OP, I have to say that there is the easy answer that god will not be tested. End of story. A religious person has this one sewn up and it does not require further explaination.
Originally when I heard this story I was impressed. I mean the only person in human history to survive Rabies is no small feet. But when I found out that they were trying a specific treatment designed to improve the odds from 0% the miracle seemed alot less impressive.