Testing 3-wire receptacles indicates no ground even though 12/2 w/ground wire is connected
The grounds should be bonded to the neutrals at the main panel.  (If it's not, it's a serious problem, call an electrician.)  If you are getting good grounds on some of the outlets, it's probably bonded at the main panel.  

If the ground isn't spliced right* at a receptacle it will show no-good at that receptacle and at all the receptacles on the same circuit downstream from that receptacle.  That would be a possible explanation.  It fits with the miswiring by the previous owner.  Tracking down the bad ones can be a bear.  Still that may be better than tracking down and replacing a damaged wire.  

*edit:  by "spliced right" I mean all the ground conductors of all the cables and all the ground terminals of the devices are bonded together in the box, and the box itself it's a metal box ... 



If there was some creative wiring going on, some wiring can cause the receptacle tester to show a good ground where there isn't.  For example jumpering the neutral to the ground terminal on the receptacle (non-code and a very bad idea) would show a good ground on the tester, but there isn't.  

If you can double check with a different tester, that might be a good idea, you don't want to chase your tail if the tester is no good.