I have 2 kids and I have some sympathy for the family and I can say that before having had my kids I wouldn't have.
4 kids here and I have to agree with that... it's kind of appalling that so many people believe a 2 year old is not really a person and has no memories that hold any value, but I suppose I can understand how someone that has had only brief interactions with 2 year olds can think that. A 2 year old is definitely a person with thoughts, feelings, memories, and a personality, and if I lost one of mine at 2 and thought there was even a slim chance at preserving them, I'd do it. I still think it's rather silly to get all attached to fetuses and embryos though.
How much do you remember from before the age of 3 or 4?
Not very much NOW ~26 years later, but ask a 3 or 4 year old how much they remember about their life and they can tell you quite a bit.
I'm guessing the parents' hope is that advancements would happen within their lifetime so that they get to continue raising their daughter from where they left off; not so much that their 2 year old has some kind of knowledge or memories that will make her important to the future.
Most people don't remember events from when they were 2 years old.
When they are still 2 years old, they do.
That doesn't mean you should accept money from desperate people when you know they will never be brought back to life.
Why not? If it makes the desperate people fell better to give away their money, why should it not be accepted?
Remember to say hello to your bank teller.