I'm a woman and I believe that if a man has asked her out HE SHOULD PAY. I can understand if a man doesn't want to cough up a fortune on the very first date with a woman he barely knows and takes her to a more reasonable restaurant. After all, no woman wants to be bought off or feel pressure to sleep with a man just because he paid. That said, being a cheap stake especially when you can afford a nice place or high-end activities is also a huge turn off and any self respecting woman would be angered/unhappy by that.
I would not jump to the conclusion that not paying for dates leads to sex. Correlation IS NOT CAUSATION. You would have to do a real EXPERIMENT to actually prove it instead of gathering anecdotal evidence from friends or personal experience. It is possible that you have forgotten to account for times you DID pay and still slept with the woman. As others have pointed out, it could just be that more good looking guys tend to not pay and get away with that behavior and manage to bed girls. Nothing to do with money, everything to do with looks. It could be confidence level of the guy or just the lack of desperation that someone who was paying and was therefore eager to please would not show.
I believe this advice is dangerous and does a disservice to people. There is a reason why men have traditionally paid and that is not just because of social norms but biological reasons-men are the hunters, pursuers and it is in their genetic make-up to be the provider/protector and even in case of casual sex, demonstrates high status and power or alpha-maleness. Paying for a date is the modern civilized way of beating your chest and bringing home the meat. It is also a charming and romantic ritual that makes a woman feel treated well. Of course some women don't care or don't have self esteem and they don't abide by the rules. But this article just confuses men and women more and changing dating rituals can actually end up doing a lot of damage. Times are changing and some women have turned this into a feminist issue.
I believe a better strategy would be to stick to paying unless the woman takes it as an insult or if you find out that she believes in going Dutch. Not paying as a rule isn't going to get you anywhere.
Personally, I would not see a guy again if he didn't pay for the first date even if I offer as a polite gesture. If he made me pay--oh my--I would refuse to cover him and only pay for myself and never see him again. I'm not a gold digger so I don't mind a modest date especially if the guy didn't make money but cheapstakes are also out. I would expect a guy to invest more than money however, so paying for a date would not excuse him slacking off in other areas. It is about making a woman feel special and money is a part of it.