Open ground

[jaggedben]

It appears that the only testing device, other than the plug in tester, that the OP has is a DMM. In a number of posts it has been stated that there is continuity between the netural and the EGC.
The EGC is open and has "ghost" voltage on it. Therefore the continuity reading between those conductors, taken with a DMM, is not valid.
He is using that "apparent" continuity to base his expectations of what the circuit should be doing.

My meters will not give a continuity reading if there's voltage. They give a different sound that is a kind of alarm. So that goes back to where I said his claim of continuity (low resistance connection) being mistaken is one possibility. The post where he said the tester showed the same in every outlet is what makes me suspect it's the tester. Ggunn's addtional suggestion to test the tester in a known good outlet is apt.

 

[jaggedben]

...

I think it would be best to check voltages with a low impedance meter, ...

That's essentially what the tester is, if it's not broken.

 

[kwired]

I don't think those work when one conductor has ghost voltage.

Probably not. If it also displays a measured value it likely never settles on one value