Saints and Miracles and Attribution

There's something about which I have been wondering.
How is it ever, ever, ever possible to attribute a miraculous cure to an as yet uncanonized saint?
I find myself unable to believe that in the entire history of intercessory prayer any life and death request was ever left in the hands of single saint or probable saint, ( with the possible exception of the Virgin Mary.)
Whoever said to himself, (and necessarily to his family and friends, for the results of the trial to be valid) yes, the baby is dying, there is no medical hope whatsoever, let's all pray to So-and-So for her intercession before the Lord of all for the dear baby's recovery, since I believe So-and-So was such a good person that she is indubitably a saint -- and whatever you do, don't pray for anyone else's intercession, not the Blessed Mother's, not that of the already canonized saint whom we think of as the patron of those with this name/this nationality/this disease/this residence, not NOBODY, only pray for the intercession of this one person, so that if baby survives we can attribute the miracle to her intercession without any suspicion that someone else had a hand in it!
No cheating now!
We want this to be a fair test of So-and-So's sanctity!
?
Huh?
Think anyone in a desperate situation ever went about prayer like that?

Me neither.....
I'm not saying I don't sometimes ask the intercession of the uncanonized.
I'm just saying I wouldn't want to have any responsibility in that curial congregation.