I have a home server and a media extender but after making sure that they were not connected to the internet I did the test again and got the same results.
Sorry, forgive my lack of knowledge, but I thought that firewalls, hardware or software, where supposed to make you invisible to the outside world when you were connected to the internet?
If there is an external IP, you're visible to the outside world. Using the stealth mode could be less safe. Because it still tells the possible attacker that there is a computer in that IP address, and that the computer admin has decided to stealth the ports. If there wasn't a computer, trying to access the IP would result in a response that there is no computer in that address, while stealth results in no response at all. So the attcaker might see the machine as more interesting challenge, something worth trying to hack into.
"Closed" port send a response to the sender that the port is closed/inaccessible while a "stealth" port doesn't send any response. So when you speak of being secure, you could just "Close" your desired port so nothing will even come from the outside.