It's nothing to do with the TOC - if you were employed by British Rail prior to 1 April 1996 you are entitled to a priv Oyster under the reciprocal BR/LT arrangements. Many FCC employees will not be entitled to priv Oysters. Note that in such cases priv rate applies on LUL - not buses
Slightly incorrect, as active FCC staff members and a nominee are actually entitled to Priv rate Oyster travel on LU, Overground and DLR only. A yellow Privilege Ticket Authority Card (Ptac photocard) is issued by TfL Staff Travel, and this is taken alongside a form signed by FCC to any LUL ticket office. The discount can be added to a registered, standard public Oyster card.
This exists due to a private arrangement between FCC and TfL and only applies to FCC staff; no other Tocs have a similar arrangement.
Other Priv rate Oyster cards are issued to:
Safeguarded LUL/TfL staff/retired staff/dependants/nominees - LUL, DLR, Overground & BR
Safeguarded BR staff/dependants - LUL, DLR, Overground & BR
Non-safeguarded LUL/TfL staff child dependents - LUL, DLR & Overground