Steps to reproduce the issue

Have module options set to edit module via administrator (see screen shot)
Login to front-end
Click on edit icon for a module (see screen shot)
This next step would normally take the user to an open module for editing (see last screen shot)
Instead, it takes the user to the list of modules and gives this error:
"Error. You are not permitted to use that link to directly access that page (#90)"
The (#90) would be which ever the module ID is. (see screen shot)

Expected result

To be taken directly to the module for editing, as if I had opened it from the administrator to begin with

Actual result

Leads to the module administrator page with the error highlighted in pink:
"Error. You are not permitted to use that link to directly access that page (#90)"
The (#90) would be which ever the module ID is.

System information (as much as possible)

Joomla 3.5
PHP 5.6, also tested in 5.5 with same result
Safari 6.1.6
Firefox 45.0.1
Opera 36.0
Chrome 49.0.2623.108

Additional comments

I have tried this on three installations now and the issue is consistent. All three installations were Joomla 3.5. My other sites that are running 3.4.8 work as expected, meaning that when I click on the edit icon it immediately opens the module for editing via the administrator.