I don't get it, it would have needed to be broadcasted on both blockchains for you to access them. If you could access them on both then you could double spend.
Im missing something here.
What you're missing is that even though
the transaction is not valid on both chains, the
address is still valid on both chains.
If you are BITMAIN, you receive 1 BTC to an address generated by a BCH wallet. Because BTC and BCH use the
same addresses and private keys, the address and private key generated are valid on both chains.
Therefore, you can export the private key to a BTC wallet and spend from there.
An exception to this is if a BCH user sends to a BTC address which is not valid on the BCH chain (for example, sending to a SegWit address).