There are some places in code where maxbytes is set for filemanager as, for example, $course->maxbytes.
If user logs in as admin (or person with capability moodle/course:ignorefilesizelimits), filemanager form element tells me that file size is unlimited and I am allowed to upload a big file.
Although when user saves the form, the funciton file_save_draft_area_files() checks if filesize is not more than $options['maxbytes'] and does not save the big file.
I just fixed the maxbytes for mod_forum in MDL-33948 but it does not seem possible to fix it everywhere where filemanager or textarea elements are created. Instead I would suggest that file_save_draft_area_files() checks the unlimited capability.
Examples of such forms: mod_glossary, mod_folder and probably many others