Two things on that: firstly, we seem to get accused of that a lot, often by Hearts fans which is cute given they're the ones nursing the pathetic 40-year grudge. But perhaps there's something in it, and it's likely to have something to do with our actual rivals being utterly shite for unbroken decades. You're in a similar boat, so maybe just get with it.
Secondly, actually, my Grampa always used to talk about Killie as being rivals, mainly based on the traditional New Year games. Not saying he was correct either way, but I don't think this is a new thing.