It's not possible to load a new favicon file for a website which runs the ezwebin interface, unless you create a design extension.
The suggested solution is to override link.tpl in the ezwebin site, and to add a statement which tries to fetch the file also from /var/storage/packages/ez_systems/ezwebin_design/files/default/file/images

Steps to reproduce

1. create a new favicon
2. copy the favicon in the /var/storage/etc. folder
3. see the website still using the stock ezpublish favicon