My girlfriend recently moved into a new apartment which I have come to suspect might have bootleg grounds, or otherwise improperly wired outlets. After multiple surge-protectors said that they were not grounded she bought a GFCI/outlet tester. When plugged in the tester says that the outlets are wired correctly, but when the GFCI test button is pressed the GFCI doesn't trip and the tester changes to reading that hot and neutral are reversed until the GFCI test button is released again. Pressing the test button on the outlet itself works normally. None of the outlets have any special labels.
The building is old, and originally did not contain apartments, so it seems reasonable to assume that the wiring was in some way retrofitted into it. Some searching around on the internet has led me to suspect that these things might be symptomatic of the outlets having a bootleg ground. Is this the correct conclusion, or are there other possible causes of this?