Let me reply to your post point by point, Hannett:
I'm sorry, please don't let this degenerate into an 'Are American or European NO Fans More Dedicated?' 
That's just typical of Brits (he said, fully aware of the reverse stereotype). They automatically own New Order because they come from the same little hole of an island and the band must then somehow be speaking to specifically English/British concerns. They're just sore over New Order being lumped in with Depish and The Cure in America...which any American with ears can tell are all completely different bands.
Over here, New Order is seen as one of the defining indie bands, much less 'alternative', at least ever since 1983, when their sound became much more accessible and less awkward.
The arthouse crowd still seems to revere early NO...I recall seeing PCL as one of the top albums of 1983 in Artforum not long ago. That said, the youth (college-age and younger) here in the U.S. don't listen to New Order except for the very tiny minority like yours truly and the sort of other septics who post on sites like this because we're so fucking elite and no one else in the general vicinity to talk to about the band. Joy Division is seen as a "defining indie band," embraced by the "indie kids" as serious music, but New Order slips through the cracks as silly dance music that gets lumped in with other "new wave" groups and is not taken seriously except on the oh-so-trendy 80's nights when BLT and BM and TF are easily heard.
It used to be that indie meant you were on an independent record label, but recently the term has mutated to represent a certain sound and a specific 'look' in the States- mussed hair, dirty off-color jumpers, overly tight ironic t-shirts, etc. Imagine the convergence of the Emo style with the Grunge style wandering around uni campuses, or just look at a picture of the Bravery or the Killers 
Indie has changed into a nicely marketable stamp of approval for record companies. I still use it anyway because I'm too lazy to dice up all those bands (major label or not) into the sort of annoying classifications they give themselves ("no, we're not indie...we're post-nu-electroclash"). Naturally, there is a big-time indie "look" also...mutant spawn of lazy people.
New Order was great because they never bought into the idea of overly-stylized visual appearance being an important aspect of a band. So old alternative yes, contemporary 'Alternative' no
Overly-stylized in Saville's cover art only? Maybe not in their physical appearances.