not impossible

Hmm...I'm not sure I remember Batman Begins completely enough to make a comparison. TDK definitely has more violence than I thought was allowed in a PG-13-rated movie; the violent acts tend to happen quickly and just offscreen, but evidently they can get away with showing a good deal of disturbing buildup to violence as long as they don't show blood. I can think of one scene where I looked away the second time I watched it despite knowing that they were going to cut away right before the Joker [SPOILER]ed that guy. And there are a couple of VERY effective startle-scares.