Rent question...Should I fight the system?

A year ago I signed a 6 month lease with a shitty apartment complex. After these six months of rent were paid and complete we decided to go on a month to month rent basis. We never signed any kind of agreement or month to month "lease". We moved out of our apartment on May 1st and we didn't pay May rent without giving a 30 written notice. In April, we had a face to face notice saying we were getting out and not paying may rent. This shitty apartment complex has since been bought out by some sort of real estate agency. These new people are now calling saying I owe May rent and that if it is not paid that they would send it to collections and it would effect my credit. They're saying since I didn't sign a lease for month to month that after my 6 month lease was up, it automatically goes into a month to month payment plan agreement. I'm skeptical of believing that this is true.

What do I do here? Should I fight the system and claim that I never signed any kind of agreement for a month to month renting basis or should I just go ahead and pay the $625?