I see those sorts of prayers as more about being solipsistic than being about changing the past. I think that the person looking at the test result envelope is just thinking about what it says inside and hasn't given a thought to the fact that the envelope's contents were already determined by the technicians in the lab that analyzed the biopsy or whatnot.
Regardless of how they are looking at the situation, though, regardless of if they have thought through the implications, they are indeed praying for the alteration of the past.
Whether people knowingly ask for such things is another question, I think.
So you don't pray for the past to be changed because you don't pray for change at all?
Yeah. Why would I?? Things are fine, things have always been fine, and things will always be fine.
To those who wish things to be one way and not the other, all that can be said is "Shoo! Get back! Don't disturb the process of change!" (-Chuang Tzu)