Our old field technicians 'Bible' (The black book), actually quoted that up to 30 volts of battery contact fault would see minimal impact on PSTN services.
Of course, that would be devastating for DSL services.
Regarding test results ... you can't have a false positive with a contact result test, if one has been found then one exists.
You can however have a false negative result, this occurs when we have a 'Tapping battery contact' ... in other words the fault is there one minute then gone the next, and so on.
With any remote testing (ie: by the ISP/CP), the test they perform is a 'One-shot test' which basically means if the fault isn't there at the specific moment in time the test is run, it will return a LTOK (Line Tests OK) result. Literally a second later and the fault could be back.