Even if the anonymous user has attachment permissions they are not able to attach files to a new page via the image/link browser.

Steps to reproduce:

1) Allow Anonymous users create page and add attachment permissions to space.
2) Log out and access the space as an anonymous user
3) Create new page and click link on insert image.
4) It will not give you the option to upload a new image.

If you save the page and edit again and click insert image, then it will allow you upload the image.