Image upload not working for "AUTHENTICATED USER"
Do not give your authenticated users the Import media files from the local filesystem permission. It's actually different functionality that could open you up to security risk.

Looking at media_media_browser_plugin_info(), we can see that in order to use the upload plugin, the user has to either have the Edit media or the Administer media permission. Likely you'll want to assign the former.

I'll file an issue to correct that the import permission is misleading, and improve the description of the Edit media permission to be clear this is necessary to upload files in the browser.