Some cases probably can, but it's not very plausible that such things explain all treatment effects, which are occasionally quite dramatic. Also, many studies include a "waiting list" group to control for the effect of simple passage of time. There are of course many, many, many poorly-designed studies out there; this is not by any means unique to psychiatric drugs, or even medicine in general.
> I do think any patient that has been on a psychotropic drug(especially the addictive ones) a long time, should be able to get that particular drug without seeing a Psychiatrist. I know that will never happen on the U.S.
As far as I know, any licensed MD/DO can prescribe psychotropic drugs in the US. Some choose not to prescribe some classes of drugs (e.g. antipsychotics, MAOIs) because they tend to have more risks associated with them. However, the same can be said for psychiatrists. There are a few psychiatrists who explicitly refuse to prescribe drugs at all, except in the process of discontinuing a pre-existing treatment. Many doctors will also refuse to prescribe the more addictive drugs out of fear of enabling addiction (this is a huge problem for people with chronic pain, as is the FDA's requirement of "abuse-resistant" pills for oxycodone that just happened to be announced on the same day as the original OxyContin patent expired...)
> After hearing that Robin Williams committed suicide and the last tabs open on his IPad were the side effects of the various drugs he was taking, I wonder if he would still be alive if he didn't have access to the best Psychiatrists?
There's a risk of iatrogenesis for treatment of virtually any condition. But I think it's far more likely that the drugs in question simply didn't work for him, or stopped working suddenly (this can happen after long periods of treatment with psychotropic drugs, and as far as I know most patients aren't warned about it; I certainly never was).