I think the distinction between "true" and "non-true" fans is a little too simple and overrated. I think degree of fandom is more accurately split into three categories:
1. Bandwagon fans- These fans only care about the team when they're doing well, and ignore the team when they're doing poorly. These are the only real "non-true" fans, because they don't ride along with the rest of the fans through the lows as well as the highs. They may even more fully adopt another team in another city when they are doing better. There's not necessarily anything wrong with these people, except when they bust out the caps and jerseys during a le run and act like they've been there the whole time.
2. Casual fans- These fans probably have a few pieces of team gear, and attend at least a few games per year if they're in town. They enjoy their team and support their team, but generally their interest wanes between games. They probably acknowledge their team's shortcomings, but except in the leanest of years, generally feel that their team can win any given game.
3. Hardcore fans- These fans live and breathe the sport and the team. Their interest extends beyond game day and even the season. They engage other fans in conversation on a regular basis, and the technologically inclined of them spend a lot of time on message boards. Their analysis of their team often allows them to see every strength and every weakness of the team. While there are extreme optimistic and pessimistic hardcore fans, most tend toward realism.
Problems generally arise when casual fans try interact with hardcore fans (or, unrelated to this post, when bandwagoners interact with either of the other two). While these categories are within a spectrum, generally casual fans are more optimistic than hardcore fans. Hardcore fans analyze so much that they tend toward realism, which can seem like pessimism to the casual fan.
So, more realistic hardcore fans are still true fans, even if the casual fans perceive them as more critical of the team or having given up on the team. However, most of these hardcore fans still proudly wear their jerseys to games, cheer as loudly (or louder) than everyone else, and enjoy the wins, even if they may have lost some of that pure, unspoiled "believe" at ude.