@freakofnature okay, I just looked up the word more and learned that it can be read as しらゆ, and what you said might be right (though I don't see why you wrote its literal kanji translation instead of what it commonly means in your original comment) But I still don't see why you needed to point those out, and what you explained wouldn't really make sense in this context.
Shiota looks like the type of guy who don't cook often and thus less likely to have paitan in his fridge. And in the story, he couldn't drink beer so the next, easier alternative would be plain water, in this case hot (probably his attempt to have a healthier drink). And again, why would he use a mug to drink paitan?
Your comment would make more sense if we see him drinking from a bowl and they translated what he's drinking as hot water, but seeing that he's using a mug and considering what we know of his habits, hot water is the more likely answer here.
Though your comment is definitely helping us learn another way to read 白湯, I'll keep that in mind.