As far as 'who owns what', the blockchain has the final say. This is an underlying concept of Bitcoin.
Not true. The blockchain is a record of who possesses what. It is not a record of ownership or title.
If you send me 100 BTC for safekeeping, or loan me your car, I possess it, but you still own it.
But the proof lies in the blockchain, which says I did own them and gave them to you, in a way that looks exactly like every other transaction.
Unless, of course, you have an explicit contract involved identifying the transaction, but even then it is hard to prove.
I'm unaware of where the exchange is located, or what the laws there are... but couldn't you write off the loss on taxes?
Dangerous door you are opening up there.