Why is access to some of my product displays denied for anonymous users? I think I have some database corruption and a number of commerce display nodes have have become access denied for anonymous users. I am not using any access control modules and the problem persists even after allowing anonymous users to bypass content access control. Clearly there is something badly wrong.

I have clear caches etc, to no avail.

What could be causing this and were should I start looking for a fix?

Following the suggestions given in comments, I have tried rebuilding permissions and this does not help.
I have the same problem. It`s because product entity was unpublished.
After publishing entity all warks correct.