In the long run we must have exactly one bug tracking system. Suse e.g. have one bugtracker and use the "insider group" functionality in Bugzilla to have bug reports and/or comments/attachments only visible to employees if chosen, but they only deal with software.
Having secret hardware information too makes this a much more complicated problem to solve. Fixing some upstream issue in Mozilla Bugzilla e.g. about being able to set the visiblity of specific fields (hardware info etc) might help.

Of course I got exactly the same problem here. Often being silent by non commenting. And a small number of my "I don't know" comments in the public Bugzilla are actually lies, thanks to the NDA.