I assume because thriii wants a color in the PNG to match an HTML one (background color, for example), and if there's gamma info in the PNG and the browser supports it, it could end up changing that color.
As for the question, I'm pretty sure Photoshop's "Save for web and devices" component doesn't include any gamma info unless you check the box to include color profile--I've certainly never had a problem if that wasn't checked.
I think it's checked by default, so you might make sure it's not.