I want to know this too, altho brine has more salt. I asked slim and save if tuna in sunflower oil was ok and they said it was fine. I do drain as much as I can tho.
I'm guessing it's the salt level in the brie that might be an issue. But if so that's more about water retention than it is about fat loss - so it may make it look like you haven't lost much that week when in fact you have.
Neither have any carbs in so should be fine to keep you in ketosis but water would be better as brine has little more salt and sun flower would contain more fat and salt.
