Even then, this already happens naturally for most everyone now and again! Like the article says, this happens whenever someone goes "into the zone" - a state many professionals spend a lot of time seeking out, and those who are really good can almost slip into it at will. It does not make you start shooting people indiscriminately or otherwise turn you into an unthinking machine. :/
No, people do not naturally apply current to their brains. Maybe it's similar to a natural state that can be induced, but we should be really careful about saying it's the same.
I'm really not convinced that "background noise" is all useless. Sometimes my "background noise" stops me from doing stupid or dangerous things. Or indeed immoral things. There are times where being in the zone is useful, and times when it really isn't.
People saying that there are definitely no side effects when as far as I can tell there have been no studies into whether there are long time side effects also somewhat concerns me.
And the effects last only as long as the current does (though there are supposedly general increased mood effects for a couple hours afterwards in some subjects)
The articles you quoted quite clearly said that it's supposed to last for quite a while after the treatment (like the blogger said it lasted 3 days). If you kept having it the amount of time it lasts for could be longer.
Yeah, the article certainly oversells it, but the effect is there. And placebo is unlikely, because depending on where and how they hook it up, the effect changes, I believe. They've also run blind studies, which make it likely the effect is real.
If you tell someone that the effect is going to change when you change the input then the placebo effect will cause them to feel a different effect. Blind studies would be great - but while wikipedia mentions a way in which you could do a blind trial, I couldn't find any linked from there. When I google for double blind tDCS trials I mostly get trials saying that there is no significant difference between tDCS and placebo at treating depression, although it doesn't say anything about flow.