Pureblood doesn't make sense in the Inquisitor storyline because:
a) The unknown "Force-sensitive slave" background
b) Ffon is given special treatment by Overseer Harkun because he is a Pureblood, so it wouldn't make sense if you were one too and given poor treatment
No, you were given poor treatment because you were a slave, even if you are pureblood. And there are certainly ways of slavery being thrust upon your family, should you be pureblood. The Lost Tribe of Sith books explain that a bit.