Steps to reproduce:
1. Go to the Configure Global Security screen (http://server/jenkins/configureSecurity/) and choose "enable security"
2. Select "Jenkins's own user database" as the security realm
3. Select "Project-based Matrix Authorization Strategy" as the authorization
4. Give anonymous user the read access to overall
5. In the text box below the table, type in your user name and click "add"
6. Give yourself a full access by checking the entire row for your user name
7. Scroll all the way to the bottom, click "save"

Now, you have access to all projects and anonymous users have access to specific projects, the config.xml will have:

<authorizationStrategy class="hudson.security.ProjectMatrixAuthorizationStrategy">
<permission>hudson.model.Computer.Configure:jose.rob.jr</permission>
<permission>hudson.model.Computer.Connect:jose.rob.jr</permission>
<permission>hudson.model.Computer.Create:jose.rob.jr</permission>
<permission>hudson.model.Computer.Delete:jose.rob.jr</permission>
<permission>hudson.model.Computer.Disconnect:jose.rob.jr</permission>
<permission>hudson.model.Hudson.Administer:jose.rob.jr</permission>
<permission>hudson.model.Hudson.ConfigureUpdateCenter:jose.rob.jr</permission>
<permission>hudson.model.Hudson.Read:anonymous</permission>
<permission>hudson.model.Hudson.Read:jose.rob.jr</permission>
<permission>hudson.model.Hudson.RunScripts:jose.rob.jr</permission>
<permission>hudson.model.Hudson.UploadPlugins:jose.rob.jr</permission>
<permission>hudson.model.Item.Build:jose.rob.jr</permission>
<permission>hudson.model.Item.Cancel:jose.rob.jr</permission>
<permission>hudson.model.Item.Configure:jose.rob.jr</permission>
<permission>hudson.model.Item.Create:jose.rob.jr</permission>
<permission>hudson.model.Item.Delete:jose.rob.jr</permission>
<permission>hudson.model.Item.Discover:jose.rob.jr</permission>
<permission>hudson.model.Item.Read:jose.rob.jr</permission>
<permission>hudson.model.Item.Workspace:jose.rob.jr</permission>
<permission>hudson.model.Run.Delete:jose.rob.jr</permission>
<permission>hudson.model.Run.Update:jose.rob.jr</permission>
<permission>hudson.model.View.Configure:jose.rob.jr</permission>
<permission>hudson.model.View.Create:jose.rob.jr</permission>
<permission>hudson.model.View.Delete:jose.rob.jr</permission>
<permission>hudson.model.View.Read:jose.rob.jr</permission>
<permission>hudson.scm.SCM.Tag:jose.rob.jr</permission>
</authorizationStrategy>

Go to jenkin management screen (http://server/jenkins/manage) and click "Reload configs from disk"

After it finishes anonymous users can now access all projects, if you go to the Configure Global Security screen you'll see that anonymous task read is checked

If you save again without changing anything, the config.xml will have:

<authorizationStrategy class="hudson.security.ProjectMatrixAuthorizationStrategy">
<permission>hudson.model.Computer.Configure:jose.rob.jr</permission>
<permission>hudson.model.Computer.Connect:jose.rob.jr</permission>
<permission>hudson.model.Computer.Create:jose.rob.jr</permission>
<permission>hudson.model.Computer.Delete:jose.rob.jr</permission>
<permission>hudson.model.Computer.Disconnect:jose.rob.jr</permission>
<permission>hudson.model.Hudson.Administer:jose.rob.jr</permission>
<permission>hudson.model.Hudson.ConfigureUpdateCenter:jose.rob.jr</permission>
<permission>hudson.model.Hudson.Read:anonymous</permission>
<permission>hudson.model.Hudson.Read:jose.rob.jr</permission>
<permission>hudson.model.Hudson.RunScripts:jose.rob.jr</permission>
<permission>hudson.model.Hudson.UploadPlugins:jose.rob.jr</permission>
<permission>hudson.model.Item.Build:jose.rob.jr</permission>
<permission>hudson.model.Item.Cancel:jose.rob.jr</permission>
<permission>hudson.model.Item.Configure:jose.rob.jr</permission>
<permission>hudson.model.Item.Create:jose.rob.jr</permission>
<permission>hudson.model.Item.Delete:jose.rob.jr</permission>
<permission>hudson.model.Item.Discover:jose.rob.jr</permission>
<permission>hudson.model.Item.Read:anonymous</permission>
<permission>hudson.model.Item.Read:jose.rob.jr</permission>
<permission>hudson.model.Item.Workspace:jose.rob.jr</permission>
<permission>hudson.model.Run.Delete:jose.rob.jr</permission>
<permission>hudson.model.Run.Update:jose.rob.jr</permission>
<permission>hudson.model.View.Configure:jose.rob.jr</permission>
<permission>hudson.model.View.Create:jose.rob.jr</permission>
<permission>hudson.model.View.Delete:jose.rob.jr</permission>
<permission>hudson.model.View.Read:jose.rob.jr</permission>
<permission>hudson.scm.SCM.Tag:jose.rob.jr</permission>
</authorizationStrategy>

that line is being injected when jenkin load the config.xml:
<permission>hudson.model.Item.Read:anonymous</permission>