I kind of disagree with that advice. Just because I'm at the gym doesn't mean I'm not looking for a guy. I'd be just as single at the gym as I would be anywhere else. But I do turn the 'flirt' way down, because the male:female ratios are so skewed there. I don't want to lead anyone on with too much friendliness, so I play it extra cool. The best 'flirt' you might ever expect from me at the gym would be a nod and maybe a little smile as I'm working out. On the flip side, I also EXPECT a certain amount of attention from the guys there. I'm something to look at, that's how it is, and we all know it. A guy would need to display some extra interest to get me to reciprocate (if I'm interested back). Just go for it. You'll never know unless you try, at least with girls like me.
Also, I'm one of those intense looking girls, who's there on a mission (I am), headphones in, sweating buckets. It's who I am. I probably look totally unapproachable. And, when I'm doing my workout, I don't exactly want to get into a long conversation no matter how cute you are, but I'd never be irritated by someone who interrupted me briefly with a question and a smile, or who had a quick word while I re-fill my water or wipe down a machine... just don't hold me up more than a couple seconds. If I'm interested, you'll notice that those opportunities for a quick word are going to start coming up a lot.