Clearly that's not true, or the CMs on the DIS would not regularly discuss the Characters in the way that they do.
CMs in entertainment can get in trouble for loudly proclaiming "there are 42 girls who play Snow White" in front of a group of children. No one would have gotten in trouble if a CM had discreetly said to the parent, "Snow White is also available at location ABC".
It's kind of amazing where Snow White can pop up if she's needed.
A MUCH better response from any of the character CMs would have been to apologize for not telling the OP sooner that Snow White was unavoidably delayed and wouldn't make it out. After which, the CM could have mentioned the other princesses at Epcot who were available and where to find them. They could have also suggested that the OP stop by Guest Relations in Future World to find out if Snow White would be available later in the day (provided she was feeling better / was finished helping the Dwarfs). They could have even offered to call themselves, since there's a phone right behind the wall, and it's a pretty quick call to find out if Snow is planning to be anywhere else that day. And a really over-the-top response would have been to find out where the OP and her daughter were staying so that they could send over one of the autographed postcards that they have piles of backstage.
All of the things I (and others) have listed are
normal Disney-level service and have nothing to do with whether or not the child is considered a "snowflake" (which is a completely overused term that I really hate). The CMs in this situation had many options other than just shrugging and going upon their day, particularly since they hadn't bothered to come out at Snow White's scheduled time and let people know that she wouldn't be out.