Petra,
I'm not on version 10.1 yet, but I'm having a hard time believing that the ArcObjects API is causing JFileChooser to crash ArcMap. Did ESRI say there was a bug in the sample code, or a bug in the ArcObjects API? When I read the Bug Report, I'm reading it as the sample is causing the problem, not the ArcObjects API.
Have you tried creating a Java Button Add-in that launches a JFrame which contains a JFileChooser? Does that also crash ArcMap?
Are you using a 64 bit Java Runtime for your 10.1 Java Add-in?