Should Read Permissions users be able to see Site Actions on site home?

Within a test site, I have a test user set to read permissions. When the test user visits the homepage to that site, the yellow up folder icon is present but the Site Actions is not visible. Should it be; and is this the default behavior for SharePoint 2010? If so, may I modify it such that it shows Site Actions and then View All Site Content? Sorry for the multi-part. Any help is appreciated.