According to IMDB Bambi was supposed to go back and find his mother in a pool of blood, and the hunter that shot her was to be shown dead after the forest fire that he started. From what I understand something lile that wouldn't have gone over too well, especially during the War, which was a pretty sensitive time anyway.
Maybe kids were less sensitive in the 90s? Or maybe it all goes back to the whole "modern audiences are more desensitized to death and violence" argument.
http://www.youtube.com/watch?v=LPTM6GpAQlE The parents at the end of this video don't seem too concerned. One of them actually compares it to Bambi, as well.