This is just not true at all?

for B to refer to A, it needs to know the transaction id.

Transaction ids are sha256(sha256(raw_transaction)) and a raw transaction consists of inputs and outputs. All this is known before the transaction gets put in a block--and has nothing to do with blocks.

Blocks and mining mitigate against double spending (...by burning an insanely huge amount of energy to do so, inefficiently. But that's a separate issue, at least right here)