Although simple mains socket testers (as featured here) are a boon when testing a new circuit, they can lead one to believe there is another type of fault with a socket than the fault that truly exists.
Many of the misdiagnosed faults are from the primary mistake on the part of the person using the tester - failure to disconnect all loads from the circuit of the socket being tested (not just from the socket itself) before commencing with the test.
If a lamp lights, this will indicate (rightly so) that voltage is still present on the socket. If a fault is indicated then further tests should be carried out to ascertain the true fault and is best done using a solid Ground connection (not Earth) as the reference.
In a correctly wired feed, the Earth and Neutral are at (for all intents and purposes) equal voltage; The Live being the one that has voltage relative to Earth and Neutral (and Ground).
With the Neutral disconnected, it can assume any potential. If the fault is toward the distribution board, the voltage on the Neutral will usually be somewhere in the region of mid voltage (i.e. approx. 115V on a 230V circuit) because of the capacitor divider properties of the wiring. This ability to either assume a voltage imposed by the tester and/or the capacitive divider would have the tester correctly show a disconnected Neutral.
However, a load on the circuit will bring the Neutral to approximately the same potential as Live (there may be a few volts difference, but nothing to be concerned about here). According to the tester the fact that Live and Neutral have the same voltage with respect to Earth will appear as if Earth has a voltage with respect to Live and Neutral (as would be the case in a genuine Live-Earth reversal) and therefore indicates this as Live and Earth reversed.