The Haunted are pretty metalcore - definitely NOT death metal. I would say Meshuggah relies more on speed metal mixed with jazz technique, not much influence from hardcore other than the vocals. As for Fugazi, I was confused with that inclusion until Brett explained his meaning behind it (in the comments). I get it, though I wouldn't really say that myself. Band's pretty good for that kind of music, though.
Anyway, here's a few bands that fit nicely under the category of metalcore without much confusion.
Rorschach - http://www.youtube.com/watch?v=Dyprzmd3rVw
(found the whole album)
Today Is The Day - http://www.youtube.com/watch?v=0WptignJ_qs
Burnt By The Sun (not as good as the above two, but this particular album still gets listens from me) http://www.youtube.com/watch?v=N9dAjKUnB68
Discordance Axis (I think they're much more grind than metalcore, but I digress) http://www.youtube.com/watch?v=mINKK1Hpm3c
This is what started out as metalcore; however at the time (and before) even stuff like D.R.I.'s speed metal albums, Leeway, Cro-Mags, etc was getting called that though. The genre has really tenuous and different roots, but Rorschach and Integrity are considered by many the archetypes of it.