Outy, honestly, I think you need to read again. NOBODY is saying that you, in your situation, should ask a child. Nobody. It sounds horrific, and as someone who also moved a child over bullying (well, there were a lot of failures, but serious bullying was part of it) I actually understand more than you probably realise, though it was primary age and the older situation escalated to something terrifying, that is very clear.
But that is a RARE situation. It's not the normal run of bullying behaviour, because most bullies aren't severely disturbed. And so on average, a bullied child - a child like your own - is really likely to be the one excluded from an otherwise whole class party. Not because they are scary or cruel or nasty or even rude. Just because they're odd, or are being sent to Coventry by the rest.
Again: in your case, asking the bully would have been a failure on your part. A serious, alarming safeguarding failure. You would never have dreamed of asking them and of course you shouldn't have. At all. It's not something I can imagine anyone arguing, actually. Any parent asking a kid who did that to their own would be a really, really appalling parent.
Nobody has called you a bully, or said you did anything wrong. In any discussion there are going to be exceptional circumstances, and yours is definitely one of them. The comments are about the average situation, and yours is anything but.
There aren't really words to express how sympathetic I am over what you and your girl have experienced. It's something that really, really scares me over my own child's secondary years, as he's vulnerable.