Flex Builder has a file that it adds all of your bin directories to in order to allow the debug player to get around the local security restrictions.
Here's a blog post on the subject.
Essentially Flexbuilder tells Flash that it should trust the bin folder... if you do a search on your development machine for the file flexbuilder_plugin.cfg, you should find it in a folder called FlashPlayerTrust in roughly the same area you normally find SharedObject files. If you open this file in a text editor, you should see pretty much every path to every bin folder for every flex project you have ever worked on. And suddenly everything gets so much clearer.
You can do as fenomas suggests and add any directory to your trusted list. You can also follow the advice from the above blog post.
So I created a new file and placed it next to this flexbuilder_plugin.cfg file, and called it MyProggy.cfg. Flash is configured to read in all files in this folder and parse all paths out of it, and any applications run from these paths will be considered "localTrusted" and will act as they would when run from Flexbuilder. Inside this text file I put one line: "c:\program files\my proggy" and saved it. I then had to restart Firefox for the change to take effect. I also had added a text label to my application and bound the text property to {Security.sandboxType}.