Could you please let me know the exact permissions you've assigned to the role?
In UI personalization -> Dialogs tab the only one which is checked is Web tab.
In UI personalization -> Editor tab "Images and media" section is unchecked.
In Permissions here the only permissions which are enabled: Content module -> Read | Modify | Create.
If I will enable "Insert image or media" in "Images and media" section for Editor in UI personalization - then everything will start working. But also image icon will show in WYSIWYG controls, which I don't want.
Regrettably I wasn't able to reproduce the issue.
Did you test it with edit contribution webpart? To allow WYSIWYG personalization for live site you need to do following:
Toolbar personalization on the live site is disabled by default. To change this, you need to enable it in your web.config file by adding the following key to the /configuration/appSettings section:
<add key="CKEditor:PersonalizeToolbarOnLiveSite" value="true" />