Sometimes Modules Anywhere doesn't work and in the source of the page I see a comment:
<!-- END: Modules Anywhere
Modules Anywhere Message: De module kan niet geplaatst worden omdat de eigenaar van dit artikel niet genoeg autorisatie heeft.
-->
Everything is done under SuperUser account. The module is sometimes plain and very simple HTML, which shows fine when I put it directly (wihout Modules Anywhere) in a module-position. So I think rights should not be an issue.