Okay I checked "C:\Program Files\Common Files\Microsoft Shared\DW\" and dw20.exe is not there. Perhaps I was too tired to really remember the location of the detection.
So yes, it must have been false. Too bad it deleted it with no way to get it back, which is... weird.
I know that I basically see Dr. Watson (as the program's full name is called) running for no reason on various computers in the past. I hope I haven't wrecked Microsoft Office...