Can I give birth at a certain hospital even though my pre-natal Physician is not staff there?

i am insured by MediCal and want to have my baby at Good Samaritan Hospital in Los Angeles. the birth would be covered by my insurance but the trouble is that they don't have any Doctors that accept MediCal for pre-natal care. i am currently already seeing another OB/GYN at a different city but I absolutely do not want to give birth at the hospital she works because their policies are not conducive with my birth plan and i really want to have a natural birthing experience that's not rushed and more on the personal side. i've checked other Hospitals that will accommodate my needs but unfortunately, there are none who will accept my insurance for labor & delivery. so is it okay for me to give birth at Good Sam Hospital even though my pre-natal Physician is not a staff member there? i personally don't think it should be a problem because in my previous birth, my Doctor was not even around and my baby was delivered by nurses. i never saw him. any advice would be greatly appreciated.