I think a lot of people start with a base configuration similar to the $650 machine (or to a base $500 machine), and increase spending on various parts in order to make the PC more like the $1250 PC, or even the $2600 PC; where they spend being influenced by their specific goals. By the time they get up to $1200-$1300, they're probably fairly happy with their results.
Any assertion that any PC with a HD7970 is a hardcore gamer is gibberish. A few years back, people were building quad Crossfire HD5870 or HD5830 PCs with Sempron or Celeron processors (why those cards got hard to find). They weren't gamers, at all, but bitcoin miners hoping to cash in when bitcoins were trading around $18 or more. Many of these people paid for their GPUs in weeks or months. There are countless other GPGPU functions that require powerful GPUs, on PCs that may never have a single game loaded on them.
...which brings up a weakness of the value analysis. If the $2600 PC can accomplish one more unit of paying work in a week (or a day, or an hour), it may very well pay for itself many times over. That's what makes such a PC a professional's tool, not just a gamer. When the measure is in dollars earned rather than just FPS, the value analysis needs to change. I'm not faulting the conclusion in today's SBM article, just pointing out that it only applies to gaming value.
Another issue is one of less definable constraints that cannot be measured easily. Space (and/or weight) and power can have tight budgets as well, one's wife or mom may impose aesthetic requirements (e.g. no glaring lights), and Dad may not want the roar of fans.
In particular, I like grumbledook's idea for mini-ITX. No, you're not going to compare it to a full tower ATX for raw power, but you can see how well it handles tasks for which it is intended, and ten to one I'll bet you can indeed get very good gaming performance out of it.