I will try to help you with this. You are not responsible for the rent of a property which you are not able to move into.
You are not responsible for the rent until you get the key.
What the agent is trying to do is cover up their own short goings because the landlord will be wanting to know why he doesn’t have rent that month which is, as you state, as a result of the agents shortcomings.
Can I clarify anything else for you?