The species co-evolved? I am assuming the early "I am a termite" mimicry wasn't very good, but neither was the termites 'not a termite' detection logic and so each incremental step of the way over 100,000+ years of evolution, they co-evolved to believe this mimicry, at a high level.

Neither party can entirely "win" in this model. At best, they get some marginal benefit in a predator/prey/host model which alters the cyclical swings of which species is higher or lower in the equipoised outcome. Over the next 1000 years, it swings the other way.