I think that the root of my problem is described in your first paragraph. I think a better implementation would be either any part-to-any part. This would solve the Asymmetrical problem, and it would also solve the case mentioned previously where a tiny bit of cover was completely blocking a shot. This might exacerbate the case where troops that are covered are otherwise treated as unprotected.
Beyond that, there are some very weird shots (impossible) shots I've seen occur, such as dual keyhole shots (I.e. through two windows at different levels, and then across open ground). I think that could be solved via a simple rules based check -- i.e. you can only shoot through a window on a different level; or at a target on a different level fro the window; at a target that is adjacent to that window.
Finally, I have definitely seen cases that break the example that Chris has given, always involving an AI shooter. I saw one last night where an exposed alien shot through a window at a target adjacent to that window; the alien definitely did not have LOS to the center point of the targets square.
All of these exception cases and bugs are happening often enough that the game isn't fun. I might be able to adjust my play-style and tactics to work around these issues (as it seems many people are or are suggesting), but I want to be able to use something like real world breach and clear tactics I learned in the army.
XCOM's abstract system for handling these things is also kind of Janky and is occasionally unpredictable, but overall seems to be more consistent.