It takes more than just 'good people skills', tact, and being a master debater to get the message across to those that aren't inclined to listen. It requires an understanding of your opponent's state of mind. If you see what is holding them back from enjoining the conversation, then you may be more successful when you broach the subject.
Kathryn Shulz, author of the Slate Blog, The Wrong Stuff: What it means to make mistakes, has a fairly clear understanding of this phenomena and explains it well both through interviews on her blog, and in a book called Being Wrong: Adventures in the Margin of Error. (Ecco Books, 2010, http://beingwrongbook.com/synopsis). There is a great interview by the KERA host of Think (http://www.kera.org/audio/think.php), Krys Boyd, that can be downloaded as an MP3 file at the PBS podcast site: http://podcastdownload.npr.org/anon.npr-podcasts/podcast/77/510036/129111964/KERA_129111964.mp3
Take a listen, maybe even read the book, and you can be better prepared to address the S-word with peers and administrators above you. Understanding how to best dissuade concerns about the subject of safety can really help to open-up the conversation so that its comfortable to all and can be discussed as needed.
If you can't talk about it, then you can't do anything to make improvements.