The word "arbitrary" has several meanings, but for each instance of its use, there is only one meaning, and the context determines which one it is. In the definition of "whim", the meaning of "arbitrary" is not one you mentioned, but this one: "Determined by chance, whim, or impulse, and not by necessity, reason, or principle". Unfortunately, that makes it a bit circular. Let's try another dictionary. Webster gives "existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will", which I think is suitable in that context.

Of course, your judgment of what is suitable in the context may be different from mine, but there is at least one thing that speaks in my favor: your very own claim that your version "would provoke stronger visceral response". Why would it, if its meaning was the same?