What? I think it's fake women saying that.
My sister was raped by her boss, so maybe she is more sensitive, but she box and spend 6 hours a week at the gym (10 hours total if you count boxing), and truly attractive males hit on her daily. Any guy who hit on her without being prompted, even the 'cute' ones (which is, to be fair, a big part of gym goers), get on her 'red flag' list, that she share with her gym and box friends. Maybe when she was younger she might have thought that.
My personal experience (which was until recently limited to feminist hippies living in vans/tents and playing guitar around a fire tbh) is the same. Just have normal conversation, a bit of small talk, listen and pay attention, flirt a bit, only show off if it doesn't break the rhythm of the moment (better yet, don't show off at all), ask for a date without saying it's a date. If it's no, it's no. Doesn't mean you can't flirt anymore, flirting is always fun (and if it's not for you, think about that: more practice!).