From thee report, as written by the pilot, it seems that they were not under the impression that FL200 would represent 2.000 ft, but they were unsure what their cleared level was and temporarirly levelled off at 2.000 ft to get clarification first. Of course, levelling of below MSA, IF not in VMC, was not a wise decision. Subsequently there was confusion in the communication with the controller, where the controller probably expected the "flying level" would mean that the aircraft had reached its assigned level. This communication mix up prolonged the undesirable situation of flying below MSA.
It is unclear whether the unsure feeling about the cleared level existed on the ground, or whether the pilot(s) had a brain fart once airborne?