That seems like a narrow concept of 'anti-heroism' IMHO. I mean, sure, anti-heroes ARE anti-heroes because they are burdened with characteristics that are antithetical to their hero role. That doesn't in my mind have to dictate anything specific. Not every anti-hero doesn't get along with good people, not all of them are partly evil, etc. Some are just cursed, messed up, have grave character flaws, or possibly even were simply faced with insurmountable moral dilemmas which they had to solve by less than savory means. Does this mean your LN 'champion' may not get along with some good characters? Perhaps, but he could also be quite charming and articulate (as an example) and get along fine with everyone. When his anti-heroic traits are manifested it may well be in a context where they are an actual asset or at least practically necessary.