Low readings between N-E could be dampness (from plastering etc), or damaged cables. However how low is 'low' ? Either way, if there is damage it is a simple matter to test individual sections until the defect is located.
Hopefully they were testing with the L&N wires disconnected from the consumer unit, otherwise silly readings between N&E are almost inevitable.
If they are testing individual circuits and getting good results, then connecting them all together and being amazed when the insulation resistance measured is lower, then clearly they have no idea how resistance actually works.
If the meter is one of the Fluke 165X series, then yes, you do have to hold the button down for insulation resistance and continuity tests. All explained in the manual.
Only pressing the button for a short time (such as 1 second or less) when measuring insulation resistance could result in low readings.
A few volts on a disconnected circuit when measured with a high impedance meter is very common. Usually caused by cables being adjacent to other energised circuits, or the house is located under powerlines etc. Easily clarified by testing using a meter with a lower impedance setting, or connecting a small load and then testing for voltage.
All of this is pretty basic stuff, and suggests that those doing the testing don't really understand what they are doing or why.