Is it true that bacitracin zinc ointment helps a staph skin infection?

It's protective. Antibacterial ointments are great at preventing infection from getting into your skin. That's why they are great for open wounds and ulcers. If you already have a skin infection, ointments likely wont help much. It may require oral antibiotics or if there is a abscess, drainage.
Yes. Otc antibiotic ointments such as Bacitracin can help with staph skin infections. If it doesn't help then you will need a prescription ointment such as Mupirocin which has more activity against staph.