What if a peer doesn't broadcast the transactions it received?
people can customize their implementation to deviate from the default, most don't, but by default, BU relays most transactions, by contrast, ABC does not relay transactions when the fees are low (a policy inherited by forking a later version of Core)
We know what happens, the transaction eventually finds the single node mining with BU, and in time it confirms the transaction.
it's actually in the best interest of the person receiving the transaction to ensure that the transaction is broadcast to a miner, most exchanges and high volume relay nodes ensure they are connected to the miners.