Rule guess:
Convert letters in koans to numbers (A = 1, B = 2, ...), sum all resulting numbers. Koan is buddha iff total is divisible by 3.
I have only checked DOGS, which adds to 45, so it's worth a try. Adding 3 of the same letter will not change status apparently.
Oh my. DOG was the passing one, not DOGS.
Some new test koans instead:
GOD
DOGC
DOGCC
DOGA
DOGAA
-- Simon