Off the top of my head, and almost likely, is the possibility that the dealer used the 6.8L oil capacity from the 3.0TFSI rather than the 8.0L oil capacity spec for the 3.0 TDI. This is pure speculation, of course. But since this is a new car for Audi dealers to service, I wouldn't be surprised if someone didn't read the manual.
The Audi A6 (C6) 3.0 TDI V6 225HP Quattro tiptronic has a V 6, Diesel engine with 2967 cm3 / 181.1 cu-in capacity. How many horsepower (hp) does a 2004 Audi A6 (C6) 3.0 TDI V6 225HP Quattro tiptronic have?
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audi a6 3.0 oil capacity