Ok, you have two issues at play. One is semantics, the other is game balance. I know many of you already know these dynamics, but hang with me.
It's no secret that BSG tries to level the playing field throughout the game, to provide for a more evenly matched (therefore ostensibly exciting) game.
So, the "resource in the red" gauge is designed as a mid-game balance to square up the two sides before the final push toward the end. Although, if the sympathizer is drawn at the beginning of the game (therefore with all resources in the blue), you ENSURE that you'll get a Cylon-helping human.
Should the Cylon side be dominating, getting a resource in the red in the process, the Sympathizer card should mechanically and thematically represent the fact that the other characters now suspect that a specific character is either a Cylon (or a human sympathetic to the Cylon cause) who is trying to destroy the fleet, but the character is trying to convince the others that he/she is still loyal (i.e. the Sharon "Athena" Valerii, yes a Cylon but trying to prove herself loyal to the fleet). Now, this may or may not be true (as the accused Sympathizer still has a Loyalty card that is yet to be revealed). He/she is put in the Brig, and the fleet must deal with the benefits of having this character in the Brig (cannot take Ship actions, only playing one card into Skill checks), OR the consequences (an unjustly accused human that can no longer take ship actions to help the fleet or participate more strongly in skill checks). But, the character's TRUE nature is not determined. So, a Sympathizer in the Brig is trying by any means necessary to get out, whether that be because they really are a human and truly want to help the fleet, or an unrevealed Cylon who just wants to get out to be more effective (i.e. be able to acquire/use a Super Crisis card).
Now, here's where I think many are missing the point of the rules phrase:
"The 'You Are a Sympathizer' card represents a human or Cylon who wishes to side with the other team."
If all of the resources are in the blue (meaning the humans are dominating), the character drawing the Sympathizer card signifies a HUMAN who is discovered and exiled to the Cylons (like Baltar's character arc). So while his card is treated as though it was a "You are a Cylon" card, he really is a human living among the Cylons, which is why he/she cannot use the Cylon Fleet or use Super Crisis Cards.. Game mechanic wise, it basically adds 1/2 a Cylon to those already disguised/revealed. But, he/she does have an extra card up their sleeve, literally. Upon going to the resurrection ship, he/she can pass off their unrevealed loyalty card from the first stage of the game to another player. If this is a "You are a Cylon" card, this is a GLORIOUS opportunity. The Sympathizer basically gets to decide the strength of the Cylon team, pulling a character over to the Cylons most devastating to the human side. Or, it further sows distrust if he/she passes a human loyalty card to another player.
So, mechanic vs. semantics is basically:
1 or more resources in red: Sympathizer is perceived to be a CYLON that is attempting to play for the HUMANS (ostensibly, unless their unrevealed loyalty card IS a Cylon).
No resources in red: Sympathizer is a HUMAN that is playing FOR the Cylons. The card is treated as a "You Are a Cylon" card only for game mechanics and defining the sympathizer's turn. Semantically you can think of it as a human who "might as well be a Cylon. Good riddance."