No, sweating shouldn't cause the water exposure indicator in the phone to turn color. That generally requires immersion. Condensing humidity (think jungle, the opposite of AZ) might do it too. Unless you were literally pouring buckets of sweat (dripping as if you'd just hopped out of a pool)onto the phone, there's no chance. Something else did it-- maybe at the factory or in transit to the store that sold it to you.
-------------------- Lisa Gade Editor in Chief, MobileTechReview