I think we are being a little hard on this woman - not everyone dates or flirts to get into a relationship. Flirty interaction or casual dating in itself can be fun as long as you don't lead the other person on by implying there is something deeper there.
I agree that flirting can be a fun activity.
But, workplace flirting has to be handled extremely carefully. For men, because it can lead to accusations of harassment, even when they thought the woman was enjoying it and participating voluntarily, and women because it can give them a bad reputation. (Yes, it's a double-double standard, but that's the way it tends to be).
So if you're flirting with someone at work, you make a move, and they say no, you assume that they really mean no, and back off any hint of flirtation. Pushing it further is just a bad idea, professionally.
As far as the psychological angle goes, sure, you can decide that men should ask women out, and if he doesn't ask you out firmly and proactively, he's not that in to you. But deciding that has absolutely no affect on how the people you meet behave, just on how you react.
For the OP, how about agreeing with your friend? "Yeah, if he were really interested in you, he'd have asked you for your number, so I guess he's no more interested in you than you are in him. Better to find that out quickly, right?" Her reaction to that will tell you a lot about whether she really believes what she's saying, or if it's just hurt ego (ie, it's okay for her to reject him, but not vice versa).