Is it a bad idea to food detox today by fasting just one day

No need to detox. Unless your digestive system is not working correctly it detoxes you just fine.

As to the skipping eating one day: There is nothing, I repeat, nothing wrong with fasting and drinking just water for one day. A whole bunch of people do it one or two days a week. It is called intermittent fasting and will not hurt your metabolism at all. In fact the whole eat breakfast to rev up your metabolism is a myth which horribly misrepresents the thermic effect of food. If you want my information you can join the Intermittent Fasting group here or check out http://www.leangains.com/2010/10/top-ten-fasting-myths-debunked.html

I saw this in your link you posted. Thanks for sharing.
4. Myth: Fasting tricks the body into "starvation mode".


Truth: Efficient adaptation to famine was important for survival during rough times in our evolution. Lowering metabolic rate during starvation allowed us to live longer, increasing the possibility that we might come across something to eat. Starvation literally means starvation. It doesn't mean skipping a meal not eating for 24 hours. Or not eating for three days even. The belief that meal skipping or short-term fasting causes "starvation mode" is so completely ridiculous and absurd that it makes me want to jump out the window.

Looking at the numerous studies I've read, the earliest evidence for lowered metabolic rate in response to fasting occurred after 60 hours (-8% in resting metabolic rate). Other studies show metabolic rate is not impacted until 72-96 hours have passed (George Cahill has contributed a lot on this topic).

Seemingly paradoxical, metabolic rate is actually increased in short-term fasting. For some concrete numbers, studies have shown an increase of 3.6% - 10% after 36-48 hours (Mansell PI, et al, and Zauner C, et al). This makes sense from an evolutionary perspective. Epinephrine and norepinephrine (adrenaline/noradrenaline) sharpens the mind and makes us want to move around. Desirable traits that encouraged us to seek for food, or for the hunter to kill his prey, increasing survival. At some point, after several days of no eating, this benefit would confer no benefit to survival and probably would have done more harm than good; instead, an adaptation that favored conservation of energy turned out to be advantageous. Thus metabolic rate is increased in short-term fasting (up to 60 hours).