Since this is actually related to the thread topic: Yes its real, and its very obviously real and jim has at no point after it was proven tried to seriously claim it was false.
The origin of the "its fake" meme was in part due to how shitty it was handled and in part due to jim sarcastically joking about the method of the dox and how scared he was over it, which his most autistic and diehard fans took as him saying it was all fake. Gator, being an even bigger autist than the average jim superfan, ran with this narrative and pushed it endlessly via the killstream because gator just couldn't bare the thought that his undoxabled internet super daddy was actually fallible. Ralph allowed this of course because it made the jim fans happy and they were a bigger portion of ralph's audience than ralph fans. Jim basically had to come on to personally tell them they were being retarded before the STFU about how jim was actually playing 4d chess and confirming a fake dox.