Originally hiding menu actions or other links can be achieved either by changing permissions - which relies on security triming, or using a custom actions (as already pointed out in the links). Programatically otherwise using Security Triming web control (most likely in the master page), but in the case of the link you mentioned it cannot be applied as the Item is added dynamically by the Publishing features.
One alternative is to simply use:
- Create a custom action to call a Javascript function (function
defined next steps)
- Create a javascript file where you put a function that Checks if the current user is in the specific Group you are targeting (each group gets a Integer identifier)
- Create a function which hides the menu item if the above evaluation is True.
For the 1st point see here http://weblogs.asp.net/jan/archive/2010/03/01/scriptsrc-referencing-javascript-files-with-sharepoint-2010-custom-actions.aspx
For the 2nd point see here http://spdailytips.blogspot.ch/2011/09/get-current-users-group.html
For the 3rd point http://social.technet.microsoft.com/forums/en-US/sharepointcustomizationprevious/thread/395fa726-94c9-4bff-9a63-4613307445aa/ has some code example to put it together for the whole Site Actions menu.