As others have mentioned it is a trademark not patent issue and the problem doesn't just go away on December the 5th as trademarks are renewable.
However trademarks have a requirement to be used otherwise they can be cancelled. If "Leonard Timepieces" have not used the word Apple or an Apple symbol on any products in recent years then Apple can apply to have the trademark cancelled. Apple were probably quietly waiting to see if "Leonard Timepieces" would renew their trademark before going to the trouble of applying for it to be cancelled.
The first thing I did was make sure that no computer had any file sharing or any other services running on it, instead users would have to share files by placing them on a properly managed server and printers had their own dedicated print server box or were replaced with network printers. All the PCs then had local firewalls enabled to effectively make sure that there were no open ports on them even if some errant software got installed.
All users were given regular user accounts, no admin access granted. Some users that were doing things like software testing who had to constantly install software were given admin access to a virtual machine so they could do all their testing on that VM.
It was decided that the offices around the world would be linked up so that direct access to the network could be obtained all over the world. Now every office just plugged their new router into the LAN and gave full access to everything. I however installed a firewall on the new WAN link that restricted remote offices to accessing only 2 servers on our network and only on specific ports to access the services that we wanted to provide access to.
I was so pleased I did all this as one day the WAN link seemed to be going slow, so I broke out the network monitor to see what was going on to find thousands of connection attempts coming from all of our international offices. As it turns out one of the US PCs had got infected with a worm and it was spreading over the whole global network. I could smugly say that apart from the slow WAN performance we were not effected at all. Our offices ran as normal while the rest of the company lost days of productivity trying to clear up the mess. It was at that point that finally the company started to listen to my calls for better security.