Would say that the films never stated that
death was a gift, whether explicitly or implicitly. Not that I would fault PJ for that, because you'd have to get into more explanation and exposition, and as he didn't even have an extra moment in ROTK to show the fate of Bill the pony, well...
Boromir's death was well done in that it did show his passion, his repentence and redemption, his belief in Aragorn and the acting abilities of Sean Bean - I actually liked the character more than when I'd read the same. And he and Aragorn could have a touchy-feely moment without anyone thinking that these two weren't real guys. Cool.
Regarding the Rohirrim chant, what the movies showed (maybe more so than the books) was that the Rohirrim expected to die that morning. It was like they were saying, en masse, "well, the situation's bad, there's no way we can win, we're going to die today anyway so let's go and kill as many of those foul orcs as possible and not worry about anything."
It's something to which I can personally relate (not that I've been in any siege-breaking lately) as, when faced with an upcoming bad situation, I try to imagine the worst possible outcome and prepare for and make peace with that. This removes much stress and worry and allows me either to deal with the situation or even push for a better outcome.
Note that I don't shout "DEATH!" when on a deadline at work - my coworkers are already spooked enough as it is.