There seem to be two categories of response to this question. One looks objectively at the origins of the story and its performance history. The other takes a more subjective point of view, looking at what major Giselles have felt and performed on stage, what makes sense or does not make sense to the individual viewer.
Both approaches are full of possibilities.
I confess to being one of those who hasn't given much thought to these matters. Perhaps it's the inherent improbability of so many Romantic-era operas and plays, not to mention ballets, that I've seen over the years. With such works, I've become conditioned to accepting ambiguities and contradictions on stage that I would not be willing to accept in life.
As several posters have implied, it's probably a good idea to examine the work from the point of view of 19th century audiences, even if we then decide to follow a different interpretive path. I especially appreciated insights about performance history such as those below:
I read, in Ivor Guest's book on Giselle, I think, that originally in France she did stab herself, like Marc says. Then when Giselle went to Russia, she wasn't allowed to kill herself on stage due to religious proscriptions.
Is it possible the original creators Gautier et. al. didn't really think through all the details completely?
Gautier et al. probably didn't think through all of the details, but the problem is also that we don't really see what they were thinking about, or intended. Giselle has been handed down and altered.
We have no censorship on these issues today, at least not in the Western world. Audiences either lack theological interest in these topics or are accustomed to separating their own value system from things that they see on the stage. This leaves us with the matter that interests me the most -- what works best on stage? I like the idea of allowing the individual ballerina to choose her own method of death -- the one which she can portray most effectively.
I have a very clear memory of reading that the suicide death was deemed necessary for Grisi because she wasn't a strong enough actress to carry off a mad scene and a les concrete death, but when Fanny Elssler got the role she, in effect, said, "La Elssler does not need a sword to die!" and, voila!, we have the mad scene we all know and love today. This would match the inconsistencies in the libretti -- the original, nonsuicide one submitted to the Theater and the slightly later one that matched the stage action.