Haleivi
I was right about Tamei oil. Below is a cut and paste from Havolim. Btw he has good schoirah on this topic.
The rule of Tumah Hutrah Betzibbur is this: Generally, the Kohanim who do the Avodah and the ritual objects which are used in the Avodah, must be Tahor. If, however, the majority of the Kohanim are Tamei, or if the Korban itself became tamei, or if no oil/flour/wine is available which is tahor, then we invoke the rule of Tumah Hutrah Betzibbur, which allows us to disregard Tumah problems.