Can an outlet be grounded without a ground wire?

I live in a rental apartment built in the late 60s and the outlets are all two prong. A few years ago, a repairman put a 3 prong outlet (not GFCI) in the master bedroom and I've been using a window air conditioner on it without a problem. However, upon recent inspection, I turned off the power and looked at the outlet and noticed there was no ground wire. But with the circuit tester indicated that the outlet was grounded. Is this possible? Also, our electrical boxes are metal if that makes a difference. And is it safe?