I suspect they're approaching it from this perspective:
As a landlord you have a duty to mitigate your damages by seeking a new tenant. The former tenant would normally get credit against the balance they owe for any amounts you collect from the new tenant.I don't agree that you should have to rent at the same rate (or a lower rate) if you are seeking a new long-term tenant and not just somebody to finish out the former tenant's four remaining months. Admittedly, I have not researched California law on this issue. If you're seeking a replacement tenant on a longer-term lease (e.g., a one year lease or 18-month lease), I would tend to think that you would only potentially relieve the former tenants of their obligation if you were trying to charge an above-market rent which minimized the chances of re-renting during the four month period at issue.
If you put the house up for sale and are not seeking a new tenant, you are not attempting to mitigate your damages.
If you seek a tenant at a higher rate of rent than was paid by the former tenant, you have a reduced chance of finding a tenant.
If the only thing that will make the property management company happy is your charging the exact same amount of rent, and you don't want to have a local lawyer write them a letter clarifying your rights under the law (to the extent that they are in fact wrong), perhaps they would agree that you could either seek a short-term tenant to finish out the four months at that same rate of rent, leaving open the possibility of a longer-term lease at the end of that period, or seek a longer-term tenant while offering a "rent sale" through the end of the first four months followed by a bump up to a rate which reflects the current housing market.
The suggestion above is worth trying, also - ask them to produce their legal authority.