Can I Feel Secure On A Shared Server

I have a small reseller account but all the domains are managed by myself. Security has not been a problem because the sites are simple, but now I have a need to deliver and recieve private files. I know how to keep the website itself secure writing my own sessions, using explicit variables, storing sensitive data outside of the web directories and that sort of stuff but it is my 'neighbors' that bother me. If one of them gets hacked or I get a bad neighbor sharing the server I do not want them to have access to my files and passwords.

A few years ago I wrote a browsing script that I found out had the ability to escape my own area and roam freely around every area on the server with unlimited access to every file. When I complained about it, the server admin said that I had nothing to worry about. When I pressed the issue I was told that nobody could invade my files because it was against the rules to go into other people's account. It turned out most server administrators left things open to eliminate scripting problems for their users and there was really no way to lock down a server without breaking a lot of scripts. At the time I moved to a more secure server but they eventually opened things up because of too many complaints and help requests.

Have things changed? Have they worked out the issues with shared servers? Is there a way to tell if my host has implemented proper safeguards (if any viable ones exist)?