Yes, this is TRUE. Master pages and page layouts along with themes are the main elements of the Site Branding. The most important thing to know is that master pages and page layouts are not compatible between versions of SharePoint. For instance, 2013 master pages content place holders have undergone changes from 2010 and between 2007 and 2010 a new ribbon has been added to every page. Therefore, it is strongly advised to not migrate them when moving to a newer version of SharePoint.

a