Steps to reproduce the issue

Sign in as "Administrator", without "Superuser" rights into the back-end.
Go to "Extension Manager > Templates" and click on a Template to view and/or edit the CSS files

Expected result

Three tabs: "Editor", "Create Overrides", "Template Description" and a list of files, ie:

admin
css
css-compiled
custom
features
fields
fonts
html
images
etc.

Actual result

I get one tab: "Template Description" and no files.

System information (as much as possible)

The hosted system:
PHP 5.5.28
Joomla 3.4.3

I've been able to reproduce it on my local system (Mac):
PHP 5.6.3
MySQL 5.6.21
Joomla versions: 3.4.2, 3.4.3, 3.4.4

Additional comments

The "administrator" does not have a problem on version 3.4.1.
The "superuser" has no problem accessing the CSS files on any version.

I've cleaned cache, tried three different browsers, and enabled/disabled the "Preview Module Positions" with no difference.

Is this a new security measure? I most likely won't be permitted to be a superuser on the hosted system, but I need to be able to edit the CSS files.

Thank you,
Mary