I've no idea how JCE handles its conditioning. If it was implemented the same way TinyMCE has it implemented it should work fine as we're just calling Joomla's API as follows.
Code:
return Editor::getInstance( $editor )->display( ... );
Basically we've implemented the usage to match Joomla's editor fieldtype. Reviewing TinyMCE it's properly using the viewing users account to determine access. I'm not sure what JCE is doing, but it might by trying to use the $author property, which shouldn't be used for editor permission checks.
Be sure your global editor within Joomla global configuration is set to JCE as that could be the possible cause if it's set to something else.