I don't think it's "either a myth or a reality", I think it's probably a mixture of the two, an exaggerated truth (although I think you'd find it very hard to define a pop band seriously as fascists). Most likely they were young and a bit naive and just jumped upon influences and imagery that appeared powerful, different and cool and a bit dark to them without ever really considering the connotations or repercussions of choosing a name like Joy Division, and later, New Order. I know Peter Hook later defended the choosing of the name New Order, denying they had read Mein Kampf or even knew of the associations.
However, I think during Joy Division's press at the time, there were quite a few reports of possible fascistic tendencies, so they certainly weren't unawares of the speculation. Ian Curtis had apparently read the book The House of Dolls by Karol Cetinsky and lifted the name Joy Division from there.
If they were, perhaps misguidedly, influenced by Nazi culture and aesthetics, they certainly weren't the only ones. Bryan Ferry was recently in trouble for praising Leni Riefenstahl's films, and certainly young, wannabe dissident lads have a tendency to view Nazi ideology and aesthetics 'ironically' as cool and a bit different. But I reckon it's something that people grow out of. You can perhaps see why an indie band would be attracted to certain aspects of the Nazi propadanda campaigns, ie. strong signs and imagery, contrasting colours, mass rallies etc. It's a good way to be noticed, but I think even if you could prove that Curtis tucked himself in bed at night with a cup of cocoa and a copy of Mein Kampf, it would still be a bit of a stretch to define them as fascists. Given that fascism is a political ideology and thus, strictly speaking, one would have to be a practioner of that political ideology to be a fascist, and not just someone who occasionally swooned over swastikas or Albert Speer blueprints and had general sympathies.
Also, fascism as an ideological stance often involves the hatred and ostricisation of those who represent change and difference, and I don't think Joy Division or New Order's music reflects this, far from it in fact.
Interesting debate though. And I agree that it wasn't exactly circumspect or well considered to be aligning oneself with Nazi aesthetics and ideology, but no, I don't think Joy Division or New Order were fascists. But I won't hold it against them - they made some damn good music.