The first problem you mention, of falsely marking bugs as duplicates, might be helped by having a 'not-duplicate' field in the bug tracker to complement the 'duplicate' field. So as well as writing in the description 'this is not a dup of #123 because...' you would also encode that information in machine-readable form as not-duplicate=123. Trying to mark it as duplicate would require an extra explicit step to override that marker.
I haven't used Launchpad's bug tracking, but I suspect the problem is in user interfaces that present bugs as bad things or todo items, and closing bugs as a good thing. Instead of the aim of the process being to improve the software, the aim becomes to close as many bugs as possible. You get a good feeling from marking a bug 'dup' or 'wontfix' or 'needinfo' and it disappears from your todo list. It feels like an annoyance when the pesky reporter comes back and asks for it to be reopened.
In my view the most useful thing that non-programmers can do with a bug report is to reproduce it. Not to ask the reporter whether it still occurs in the latest version, but to follow the recipe themselves and report whether they can verify the bug. If the instructions on how to trigger the bug are not clear, then of course the triager can ask for clarification.
Making a bug reproducible is often the hardest part of the process; once you have a test case for reliably making a bug appear, fixing it is often trivial.
So I would suggest the visual rewards given by the bug tracker for making progress on bugs should be weighted towards activities that add value. A bug's possible states might go through
unconfirmed, but has a recipe to reproduce it
confirmed (by N separate people)
test case written
test case confirmed as valid by upstream
Each of these states is better than the previous one and could be displayed appropriately (perhaps a 'golden bug' for one that has a test case). However it works, the interface needs to give the perception that while bugs are a bad thing, bug *reports* are a very good thing, to be nurtured, tested and reproduced, not closed.