Can an independent institution run experiments without IRB approval?
I'll address the academic, rather than legal aspects of the question.  All legitimate scientific journals require ethics review for published human subjects research.  Any human subjects research which is has not passed ethics review must not be published.  In my opinion, any such research is not part of main-stream science.  So the answer is no.
It is generally accepted that these are not research, and therefore not human subjects research:

Testing a commercial product to see if customers like it.
Experiments whose results will be kept secret.

However, all activities need to be ethical, even if they are not subject to IRB requirements.