Hi Sarah,
I assume that you are a tenant under a lease agreement with the landlord perhaps via an agent. The lease agreement is very likley not to involve the Owners Corporation, except for the fact that you will need to abide with the By Laws.
I suggest that you read the lease thoroughly. Do not be afraid to read it. If it does not say that you need to remove furniture at your cost in such situations, then ask the landlord/agent where in the lease it requires you to do this. If they can show clearly that it is your responsibility, then you will need to comply. If it does not, then you should challenge it and refuse to comply with their request unless they can demonstrate it is in the lease.
Please remember, the lease (or the contract governs), not comment or hearsay. If it is unclear, ask for clarification from the landlord, not the OC as you have no contractual relationship with them.
I would suspect, although not certain without reading the lease, that you would be required to provide access only, but not to incur cost of furniture relocations.
Good Luck,
Rob