This is the promise of things like the Oouya console but they have yet to be proven commercially viable in the market.
There are some interesting forces at work here. The amount of time and effort needed to build a truly cutting edge game console has historically been high, further tools to get the most performance out of the hardware have required similar investments in expensive engineering time. This combined with selling the consoles into a very price sensitive market.
In order to recoup those costs, given the market realities, the console makers have traditionally resorted to extracting a 'tax' out of the game developers. On the theory that charging a few extra $ for your game to cover the cost of the tools / access is possible, whereas trying to fund the tool development on the back of base console sales is not possible.
Historically this has been the PC's "secret" weapon against game consoles for a long time. The cost of building tools was offset by developer fees across a much wider base of developers. "Free" tools were good enough if the hardware was sufficiently over powered, and gamers would spend $3500 on a machine that "normal" people would budget Then there are the phone games, which like PC games, have the advantage that the phone is useful for other stuff and there are more developers trying to write apps for it.
Ooya's promise is that the existing Android infrastructure / developers will support tool development, and the wide variety of handsets will constrain there efforts to work on systems that are similar to the modest abilities (relative to all android platforms) of the Ooya console.
So to respond to the articles point, the reason you cannot write a game for Xbox using $100 worth of tools is because if Microsoft only got $100 from everyone writing a game for the Xbox you would not have enough money to actually create the tools, much less support them decently. Their best effort at this was XNA but they have since killed that due to lack of adoption, if you are EA you can pay big bills, if you aren't, there are not enough of you to pay any bills.