So answer me this if I die of hypothermia soon after eating a great prime rib dinner from the Cracker Barrel in Paradise Utah. Did I die from a full belly of prime rib or did I die from exposure?
Since I was knee high I have been involved in feeding wildlife in one way or another. Deer, Elk , Birds. Yes I have watched as (even though they were fed) some died. However, most the time is was not due to the feed but other circumstances, i.e. long term extreme cold, or starvation. You are correct in assuming that if a deer in poor enough condition to die then is fed hay or anything else in order to save them chances are high they will still die. However, if a deer in decent condition is transfered to a supplmentary hay diet be it their choice or our choice not only will they survive they will carry fetuses to full term.
Think of a person with an eating disorder either way too much or too little. As they receive treatment an extreme change is not instituted, but a gradual modification of diet is implemented.
It is much the same with wildlife a gradual change is what is need to allow adjustment, this type of program will allow most ungulates to eat digest and metabloize most forage.