re: Rent question...Should I fight the system?

Read your lease, it covers all of this.

Generally, residential leases automatically become month to month after the expiration of the lease term. Your actually staying in the apartment, and them letting you stay, constitutes agreement.

Generally, 30 days WRITTEN notice is required to end a lease, even if the lease has become month to month via staying in the apartment.

Is the person you spoke with telling them you were leaving still with the new company?

If the company calls you again, I would demand that they send to you proof that you owe them any money. They will have to dig up the old lease and have to dig up proof that you lived there, when you moved out, etc. I would also ask them for their address on the same call. After the call, send them a certified letter asking for the same, and demanding that they not contact you again until they provide the requested documentation.