z-index Drupal 7 Skeleton Boilerplate discriminating roles?
I was too quick to post the question and I apologize, since the answer is all over the internet, and for those going through the same issue:

YOU MUST add position relative or absolute to all items involved in the z-indexing. Ot the z-index won't work.

Also why was Firefox not rendering things right? I had added a skeleton class to the search box template, but had not added a clear right after.

As to why it was rendering things right when i was logged in as an admin, but not when I was anonymous, remains a mystery. 

Hope this is useful for those having identical issues.