Yes it does, if one website is penalized by Google and you both are sharing the same server then this is possible.
You're wrong. A server is not a website. Servers can host thousands of websites. Several websites can get penalized, not EVERY website on the server because of some.
Creating backlinks from one server to many sites that you own can potentially be bad! Is that statement incorrect? I mean if I own 1000 websites on a dedicated server and link to all my others sites linking back to me again this could be considered as something bad right?
No, google doesnt for a shared server. But shared ip is a different matter, always get a dedicated ip as long as you can justify it to your provider.
Probably more than 95% of web sites are on shared servers. Shared IP's also are not a problem. What is a problem if you have several sites on the same server with the same IP and you are linking between them.
I see, you are referring to a bad neighborhood. My apologies. I am referring to just being hosted on a shared server.