That most likely IS a bug if that's true, since 1) it's not stated like that (it says damage dealt in end screen, nothing more nothing less) and 2) it was not so before (my first 2k badge was obtained in a longbow-kraber poke game where I got 9 kills in the end, so if only killing damage counted, that would not have been 2k (9 kills = 1800 max, but it was 2400-something)).
And when I think about it, it's really not like you say. Since if only killing-damage counted, you would always see 0 damage when you die without killing anyone - it is not so. You do 10 damage, die, see them live happily ever after, leave and see that 10 damage on the end screen.
And if you mean damage on knocked down targets doesn't count - yes that's true, but it doesn't count anywhere, not for missions either.
I gave the mission discrepancy as just a very clear and simple example, but if you manually add all your shot damage throughout the game, I'm sure you will often get a much higher number than you see on the end screen.
