Does your lease call for a one month rent termination fee? If it does it has nothing to do with what the landlord said.
The landlord has a duty to mitigate his damages, which means if you break your lease he has a duty to try and get the unit rented. The exiting tenant would then be responsible for the time that the unit was empty.
You speak of an irrational neighbor. Was this neighbor a tenant in the apartment? Did you complain to the landlord about this neighbor? You may have had the right to a constructive eviction.
Consult an attorney in your area and have him review the lease. Many attorneys offer free consultations.
Note this answer does not constitute legal advice, and should not be relied on. Each situation is fact specific and court specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship
Nom there is no such law in California.
The amount of monetary consideration for a lease termination agreement is fully negotiable. It is not set by California law.
In your case, you negotiated and agreed upon a one month equivalent as the consideration. I think it is more than generous for the landlord to agree to accept only one month. Taking the worse case scenario, the landlord could have left it open and shifted the risk of finding (or not finding) a replacement tenant to you. Under such circumstances, your liability exposure is substantially higher. Count yourself lucky.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.