Possible solution found, RE: Java JRE 6 Update 21 - 22 RS Problem
Our company has been having the same problem as was originally described in the thread called:
Java JRE 6 Update 21 - 22 RS Problem
Today I believe I found a solution and wanted to put this out here in case it would help others.
Create a file called crossdomain.xml in the root directory of the website that is broken.
Here's a site that explains how to create one of those and what to put in it:
CurtisMorley.com » Flash / Flex Tutorial – How to Create a crossdomain.xml file.
I created that file for our website and now remote scripting is back to working, even with JRE 6 Update 23.