Here are results from my "experiments":
Exp (1) Under Module Settings -> Page Settings -> Basic Settings -> Module Container: selecting a container does not work! and has no impact on module container for Edit Control
Exp (2) Page Management -> Advanced Settings -> Page Container: selecting a container does not work! and has no impact on module container for Edit Control
Exp (3) Site Settings -> Basic Settings -> Appearance -> Admin Container: selecting a container does work; now both View and Edit Controls of module display desired container
So these experiments confirm your remarks about Edit Controls of modules processed as Admin content. In my opinion, these inconsistencies in the user interface and programming logic need to be improved. Why provide the user interface controls relevant in Exp (1) and (2) if they do NOT work? Alternatively, why force all Edit Controls of any Module to be considered Admin content?
I have looked in both online documentation, and the Wrox textbook Pro DotNetNuke 4, and have not yet found clear and cogent discussion of interaction of security permissions (View/Edit) vis-a-vis Page permissions, Module permissions, Module control keys, and whether or not controls can be accessed with or without the relevant skin and container and/or display of the Control Panel. And of course, the Control Panel is displayed in its full form or limited form (Mode View Edit only) depending on whether the current user has Administrator privileges or not. Is anybody working on developing more transparent and cogent documentation for these matters? Such documentation is necessary to better understand what is design flaw and what is programming bug....
Meanwhile, in the scenario I'm interested in, I want registered users to have Edit access to the Module but not to the Page. I also want these registered users to have that Edit access by default without any display of the limited form of the Control Panel which adds an extra step (necessary to switch from View mode to Edit mode) just to get to add content in the Module. Documentation and discussion of these matters would be greatly helpful, but again I have not found anything in either *.pdf guides on DotNetNuke website or in the Wrox textbooks.