[wyattpeak]

I think it's more accurate as it is. Your alternative suggests to me that both contribute independently i.e. chlorine alone will burn eyes, where the article suggests that isn't true.

Since chlorine in pools is ubiquitous, the urine's the central issue. C.f. hydrogen tanks being labelled "fire hazard", not "fire hazard in an oxygen environment".

[tomclive]

Maybe, but it's not only urine that causes red eyes. When chlorine binds with any organic matter it can create compounds that sting your eyes. Sweat isn't as eye-catching as urine.