I believe wrt to this article, the counter offer they are talking about is a counter offer from your current employer, not a counter offer from an interview.
But from someone who has done his fair share of hiring, I'll tell you that I almost never entertain someone who asks for a lot more than I'm willing to pay. The reason is that you are very likely to be unhappy with your salary. No matter what your performance is like, you are probably going to be asking for a top up soon -- probably with extra to make up for the perceived deficiency when starting. No matter what deal we strike, this is going to be a point of contention going forward.
And while it might be uncouth to talk about it in these circles, if you are unhappy then you're going to complain to everybody around you about how little you get paid. If you are experienced and talented and worth a good salary, then you are likely already going to be paid a fair bit more than the average person on the team. So the result is that I've got an unhappy guy wandering the halls complaining about how ridiculously small his salary is, when it is already one of the highest on the team.
And then, when someone else on the team comes in and says, "alex-yo is getting X more than me and I'm way better than him/her", I have the distinctly difficult conversation where I have to tell them, "No. alex-yo gets paid a lot more than you because he/she is more experienced and has more skills than you. Let me enumerate all of the situations where alex-yo is performing better than you." And then that person, despite potentially being educated about where they can improve, is likely pissed of at me. So then they'll go to you and say, "Geeze, I'm only making Y. I should be getting paid at least as much as you." And you will be going, "....." because you know as well as I do that this person is only doing half of what you do.
At which point I have a bunch of guys pissed off at their salary, pissed off with me and pissed off with each other. Seriously, it's not worth it. So no, I'm not going counter your very high expectations with a low-ball offer. There are other candidates whose expectations are in line with mine. And even if you are worth the money, it won't be worth it for my team.
Which is not to say that we shouldn't always be showcasing top performers like alex-yo and encouraging the team to adopt similarly successful behaviours. And it's not that we should not be rewarding people who succeed in getting to the next level. But I'm not about to start hitting hornet nests with sticks for no good reason.