I'm no biologist, but it's pretty easy to imagine a plausible mechanism.

Stress doesn't cause your body to "immediately grenade itself", it causes gradual problems over an extended period. But you can imagine that evolutionarily speaking, a stressful situation would frequently be a situation involving imminent danger. A response that prioritizes short-term survival (e.g. releasing adrenaline and cortisol) regardless of the long-term consequences could easily improve evolutionary fitness.