I think you've misunderstood the situation a bit.
The airline almost certainly allows peanut butter on board along with any other condiment. They have no reason to disallow this unless they have specific rules to avoid food allergy problems.
You were referred to the airport because the more important factor is what you can take through screening at the concourse entrance. For instance, US TSA would probably consider a jar of peanut butter a gel or paste (crazy, but that's the Government) and confiscate it. Whole peanuts are perfectly fine.
Consider, you can purchase any number of liquids in the terminalat or near your gate to take on the aircraft, you just can't bring them into the terminalconcourse yourself.